{"id":12747,"date":"2014-01-31T21:28:19","date_gmt":"2014-01-31T21:28:19","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=12747"},"modified":"2026-03-26T13:04:03","modified_gmt":"2026-03-26T18:04:03","slug":"multiples","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/multiples\/","title":{"rendered":"Multiples"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_L6CyQT10Yac\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_L6CyQT10Yac\" data-source-videoID=\"L6CyQT10Yac\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Multiples Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Multiples\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_L6CyQT10Yac:hover {cursor:pointer;} img#videoThumbnailImage_L6CyQT10Yac {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/727-multiples-and-factors-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_L6CyQT10Yac\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_L6CyQT10Yac\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Multiples\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_L6CyQT10Yac\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_L6CyQT10Yac\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_L6CyQT10Yac\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction C1t_Function() {\n  var x = document.getElementById(\"C1t\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"C1t_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"C1t\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Examples_of_Multiples\" class=\"smooth-scroll\">Examples of Multiples<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Common_Multiple\" class=\"smooth-scroll\">Common Multiple<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Least_Common_Multiple\" class=\"smooth-scroll\">Least Common Multiple<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Multiple_(PDF)\" class=\"smooth-scroll\">What is a Multiple? (PDF)<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Multiple_Practice_Questions\" class=\"smooth-scroll\">Multiple Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"factsheet\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"factsheet\">Fact Sheet<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video about multiples! In this video, we\u2019ll take a look at:<\/p>\n<ul>\n<li>What is a multiple in math?<\/li>\n<li>Common multiples<\/li>\n<li>Least common multiples<\/li>\n<\/ul>\n<h2><span id=\"Examples_of_Multiples\" class=\"m-toc-anchor\"><\/span>Examples of Multiples<\/h2>\n<p>\nSo first thing\u2019s first\u2014what is a multiple? Well, a multiple is any <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/numbers-and-their-classifications\/\">number<\/a> obtained by multiplying other numbers together.  Multiples are most commonly discussed in the context of integers.<\/p>\n<p>Let\u2019s begin with a simple multiplication table:<\/p>\n<div class=\"equationcontainer\">\n<div class=\"equationsleftside\">\n\\(3 \\times 0=0\\)<br \/>\n\\(3 \\times 1=3\\)<br \/>\n\\(3 \\times 2=6\\)<br \/>\n\\(3 \\times 3=9\\)<br \/>\n\\(3 \\times 4=12\\)\n<\/div>\n<div class=\"equationcalloutrightside\">\n<div class=\"transcriptcallout\" style=\"text-align: left;\">The numbers 0, 3, 6, 9, and 12 are all multiples of 3. In order to obtain them, 3 is being multiplied by another number. Any number has an infinite amount of multiples.<\/div>\n<\/div>\n<\/div>\n<p>\n&nbsp;<br \/>\nSome numbers are multiples of many different numbers. Take 12 for example:<\/p>\n<div class=\"equationcontainer\">\n<div class=\"equationsleftside\">\n\\(1 \\times 12=12\\)<br \/>\n\\(2 \\times 6=12\\)<br \/>\n\\(3 \\times 4=12\\)\n<\/div>\n<div class=\"equationcalloutrightside\">\n<div class=\"transcriptcallout\" style=\"text-align: left;\">12 is a multiple of 1, 2, 3, 4, 6, and 12. These numbers can be multiplied by other numbers to obtain 12. As a reminder, 1, 2, 3, 4, 6, and 12 would be called <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/factors\/\">factors<\/a> of 12.<\/div>\n<\/div>\n<\/div>\n<p>\n&nbsp;<br \/>\nOther numbers are only multiples of 2 numbers, for example, 7:<\/p>\n<div class=\"equationcontainer\">\n<div class=\"equationsleftside\">\n\\(1 \\times 7=7\\)\n<\/div>\n<div class=\"equationcalloutrightside\">\n<div class=\"transcriptcallout\" style=\"text-align: left;\">7 is a multiple of 1, and 7 only (1 and 7 are the only factors of 7). Because of this, 7 is an example of a <strong>prime number<\/strong>.<\/div>\n<\/div>\n<\/div>\n<p>\n&nbsp;<br \/>\nNow that we know what multiples are, here are a couple of truths to remember about them:<\/p>\n<ol>\n<li style=\"margin-bottom: 10px;\">Zero is a multiple of all numbers.  For any number \\(a\\): \\(a\\times 0=0\\)<\/li>\n<li>Every number is a multiple of 1 and itself. For any number \\(a\\), \\(a \\times 1=a\\)<\/li>\n<\/ol>\n<h2><span id=\"Common_Multiple\" class=\"m-toc-anchor\"><\/span>Common Multiple<\/h2>\n<p>\nWhen comparing numbers, sometimes they are compared by their <strong>common multiples<\/strong>, or multiples that the numbers have in common.<\/p>\n<p>Here are some common multiples of 4 and 10:<\/p>\n<div class=\"equationcontainer\">\n<div class=\"equationsleftsidelong\">\n\\(4 \\times 5=20 \\quad \\quad \\; 10 \\times 2=20\\)<br \/>\n\\(4 \\times 10=40 \\quad \\; \\, \\; 10 \\times 4=40\\)<br \/>\n\\(4 \\times 15=60 \\quad \\; \\, \\; 10 \\times 6=60\\)<br \/>\n\\(4 \\times 20=80 \\quad \\; \\, \\; 10 \\times 8=90\\)<br \/>\n\\(4 \\times 25=100 \\quad \\; 10 \\times 10=100\\)\n<\/div>\n<div class=\"equationcalloutrightside\">\n<div class=\"transcriptcallout\" style=\"text-align: left;\">20, 40, 60, 80, and 100 are all multiples of both 4 and 10.<\/div>\n<\/div>\n<\/div>\n<p>\n&nbsp;<br \/>\nWe can find common multiples of more than two numbers as well.  Let\u2019s look at 3, 5, and 9:<\/p>\n<div class=\"equationcontainer\">\n<div class=\"equationsleftsidereallylong\">\n\\(3 \\times 15=45 \\quad \\; \\; \\, 5 \\times 9=45 \\quad \\quad \\; 9 \\times 5=45\\)<br \/>\n\\(3 \\times 30=90 \\quad \\; \\; \\, 5 \\times 18=90 \\quad \\; \\; \\; 9 \\times 10=90\\)<br \/>\n\\(3 \\times 45=135 \\quad \\; 5 \\times 27=135 \\quad \\; 9 \\times 15=135\\)\n<\/div>\n<div class=\"equationcalloutrightsideshort\">\n<div class=\"transcriptcallout\" style=\"text-align: left;\">45, 90, and 135 are all common multiples of 3, 5, and 9.<\/div>\n<\/div>\n<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Least_Common_Multiple\" class=\"m-toc-anchor\"><\/span>Least Common Multiple<\/h2>\n<p>\nSometimes, we need to determine the <strong>least common multiple (LCM)<\/strong> of a set of numbers, in other words, the common multiple that has the lowest value.<\/p>\n<p>This can be done in one of two ways: listing the common multiples and factoring. Before, we listed the common multiples of two different sets of numbers. The LCM of 4 and 10 is 20, while the LCM of 3, 5, and 9 is 45.<\/p>\n<p>Now let\u2019s find the LCM of 4 and 10 by factoring. Remember, <strong>factors<\/strong> are numbers that are multiplied together to form a multiple. The LCM of two numbers is the product of the highest power of all <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/prime-factorization\/\">prime factor<\/a> of both numbers. Let\u2019s break that down a bit:<\/p>\n<table class=\"ATable\" style=\"width: 100%; border: none; margin: auto;\">\n<tbody>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px; width:50%\">\\(4=2 \\times 2\\)<\/td>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px; width:50%\">\\(10=5 \\times 2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px; width:50%\">The prime factor of 4 is 2.<\/td>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px; width:50%\">The prime factors of 10 are 5 and 2.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<br \/>\nThe factor of 2 occurs twice, so it is represented as \\(2^2\\). So, \\(4=2^2\\).<\/p>\n<p>Now let\u2019s find the LCM of 24, 144, and 48 by factoring:<\/p>\n<div>\n<table class=\"ATable\" style=\"width:100%; border:none; float:left\">\n<tbody>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">\\(24=2^3 \\times 3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">The prime factors of 24 are 2 and 3.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"ATable\" style=\"width:100%; border:none; float:center\">\n<tbody>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">\\(144=12 \\times 12=2^4 \\times 3^2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">The prime factors of 144 are 2 and 3.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"ATable\" style=\"width:100%; border:none; float:right\">\n<tbody>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">\\(48=16 \\times 3=2^4 \\times 3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"border-right: 0px; border-left:0px; border-top:0px; border-bottom:0px\">The prime factors of 48 are 2 and 3.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\nThe unique factors here are 2 and 3. The highest power of 2 is 4 and the highest power of 3 is 2. The LCM equals \\(24 \\times 32=144\\). Since 144 is a multiple of both 24 and 48, it is also automatically the LCM of all three numbers.<\/p>\n<p>I hope that this video has increased your understanding of multiples and how they work with numbers!<\/p>\n<p>See you next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are multiples and factors?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Factors and multiples are very closely related.<\/p>\n<p><strong>Factors<\/strong> are the numbers we can multiply together in order to get another number.<\/p>\n<p>The number that is created by multiplying these factors is called a <strong>multiple<\/strong>. Multiples can be found by multiplying factors, or simply by skip counting.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the difference between a factor and a multiple? <\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p><strong>Factors<\/strong> are the numbers that are multiplied in order to create a multiple. <strong>Multiples<\/strong> are the numbers created by multiplying two factors.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is a multiple in math? <\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>A multiple can be found by skip counting, but it is also the result of multiplying a number by an integer. This integer can be positive or negative. For example, \u20136 is a multiple of 3 because \\(3\\times-2=-6\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Why are factors and multiples important?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Factors and multiples are important in the field of math in many ways. For example, factors and multiples are used when looking for patterns in numbers, simplifying fractions, or when determining the greatest common factor.<\/p>\n<p>When simplifying the fraction \\(\\frac{8}{10}\\), we see that both 8 and 10 share a common factor of 2, so both numbers can be divided by 2 in order to simplify the fraction. Therefore, \\(\\frac{8}{10}\\) becomes \\(\\frac{4}{5}\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the definition of a factor in math? <\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Factors are the numbers we can multiply together in order to get another number. For example, the factors of 20 are 1,2,4,5 and 20 because these numbers can be multiplied together to get 20.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What does it mean to be a multiple? <\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>In order for a number to be considered a multiple, it needs to be the result of multiplying a number and an integer. An <strong>integer<\/strong> is simply a whole number that is not a fraction.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"factsheet-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"What_is_a_Multiple_(PDF)\" class=\"m-toc-anchor\"><\/span>What is a Multiple? (PDF)<\/h2>\n<div>\n\t\t\t\t\t<img width=\"1359\" height=\"1763\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432.png\" class=\"attachment-full size-full\" alt=\"An educational infographic defines multiples, gives examples of multiple numbers, and explains the least common multiple (LCM). It also highlights facts about zero and prime numbers.\" decoding=\"async\" loading=\"lazy\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432.png 1359w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432-231x300.png 231w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432-789x1024.png 789w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432-768x996.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_103432-1184x1536.png 1184w\" sizes=\"auto, (max-width: 1359px) 100vw, 1359px\" \/><\/p>\n<div class=\"sub_categories\">\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/Multiples-Fact-Sheet.pdf\"><span id=\"Your_What_is_a_Multiple_PDF_Download\" class=\"m-toc-anchor\"><\/span>Your What is a Multiple PDF Download<\/a>\n\t\t\t\t\t<\/div>\n<\/p>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Multiple_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Multiple Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich list shows values that are all multiples of 4? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">4, 8, 10, 12 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">0, 4, 8, 12, 16 <\/div><div class=\"PQ\"  id=\"PQ-1-3\">0, 4, 8, 18, 24 <\/div><div class=\"PQ\"  id=\"PQ-1-4\">0, 1, 2, 4 <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Multiples of 4 can be found by multiplying 4 by another number.<\/p>\n<p>For example, \\(4 \\times 3=12\\), so 12 is a multiple of 4. A number like 18 is not a multiple of 4 because we cannot multiply 4 by another number and get 18 as the product.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nDetermine the LCM of 42 and 126. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">42<\/div><div class=\"PQ\"  id=\"PQ-2-2\">124<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">126<\/div><div class=\"PQ\"  id=\"PQ-2-4\">44<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p style=\"text-align:center;\">\\(42=2 \\times 3 \\times 7\\)<br \/>\n\\(126=2 \\times 3 \\times 3 \\times 7\\)<\/p>\n<p>The highest power of 2 is 1, the highest power of 3 is 2, and the highest power of 7 is 1.<\/p>\n<p>When we multiply these factors using the highest power, we have \\(2 \\times 3^2 \\times 7\\), which simplifies to 126. This means that 126 is the LCM of 42 and 126.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the LCM of 3, 5 and 8? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">120<\/div><div class=\"PQ\"  id=\"PQ-3-2\">150<\/div><div class=\"PQ\"  id=\"PQ-3-3\">24<\/div><div class=\"PQ\"  id=\"PQ-3-4\">358<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Write the prime factorization for 3, 5 and 8.<\/p>\n<p style=\"text-align:center;\">\\(3=3\\)<br \/>\n\\(5=5\\)<br \/>\n\\(8=2^3\\)<\/p>\n<p>Now, multiply the unique factors using the highest power.<\/p>\n<p style=\"text-align:center;\">\\(2^3 \\times 3 \\times 5=120\\)<\/p>\n<p>This means that 120 is the LCM of 3, 5 and 8.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nZoe has a watering schedule for her two plants. She waters her cacti every 10 days and her lilies every three days. If she waters both plants today, the first day of the month, what day will it be when she waters both plants again on the same day?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">30th day <\/div><div class=\"PQ\"  id=\"PQ-4-2\">18th day <\/div><div class=\"PQ\"  id=\"PQ-4-3\">15th day <\/div><div class=\"PQ\"  id=\"PQ-4-4\">12th day <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The cacti are watered every 10th day and the lilies are watered every third day. We can list the multiples of 10 and 3, and then look for the next day they both have in common.<\/p>\n<ul>\n<li><strong style=\"font-weight: 600\">10:<\/strong> 10, 20, 30, 40, 50<\/li>\n<li><strong style=\"font-weight: 600\">3:<\/strong> 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36<\/li>\n<\/ul>\n<p>The next day that <em>both<\/em> plants will be watered is on the 30th day of the month. In other words, the LCM of 10 and 3 is 30.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMarcus swims every third day and hikes every other day. If today is January 5 and he swam and hiked, when will he swim and hike on the same day again?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">January 24 <\/div><div class=\"PQ\"  id=\"PQ-5-2\">January 10 <\/div><div class=\"PQ\"  id=\"PQ-5-3\">January 15 <\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">January 11 <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Marcus swims every 3 days and hikes every 2 days so we can solve this problem by determining the LCM of 3 and 2. The LCM of 3 and 2 is 6, and 6 days from January 5 is January 11.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/basic-arithmetic\/\">Return to Basic Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Basic Arithmetic Videos<\/p>\n","protected":false},"author":1,"featured_media":99796,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-12747","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-pre-algebra-factoring-videos","7":"page_category-math-advertising-group","8":"page_category-multiplication-division","9":"page_category-video-pages-for-study-course-sidebar-ad","10":"page_type-video","11":"content_type-fact-sheet","12":"content_type-practice-questions","13":"subject_matter-math"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"A multiple is any number obtained by multiplying other numbers together. 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