# What are Multiples?

Multiples are sets of numbers that correspond to a base number that has been multiplied by other numbers. For example, the multiples of 3 include 3 (3 × 1), 6 (3 × 2), 9 (3 × 3), 12 (3 × 4), 15 (3 × 5), etc.; the multiples of 5 include, 5, 10, 15, 20, 25, etc.

## Free Multiples Fact Sheet

Use the multiples fact sheet below to help you get a better understanding of how multiples work. You are encouraged to print or download the multiples fact sheet with the PDF link after the image. ## Multiples

Hello and welcome to this video about multiples! In this video, we’ll take a look at

• What multiples are
• Common multiples
• and Least Common Multiples

So first thing’s first – what is a multiple? Well, a multiple is any number obtained by multiplying other numbers together. Multiples are most commonly discussed in the context of integers. Let’s begin with a simple multiplication table:

 3×0=0 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. 3×1=3 3×2=6 3×3=9 3×4=12

Some numbers are multiples of many different numbers. Take 12 for example:

 1×12=12 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 factors of 12. 2×6=12 3×4=12

Other numbers are only multiples of 2 numbers, for example, 7:

 1×7=7 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 prime number.

Now that we know what multiples are, here are a couple of truths to remember about them:

• First, 0 is a multiple of all numbers. For any number a: a∙0=0
• and secondly, every number is a multiple of 1 and itself. For any number a, a∙1=a

When comparing numbers, sometimes they are compared by their common multiples, or multiples that the numbers have in common.

Here are some common multiples of 4 and 10:

 4×5=20 10×2=20 20, 40, 60, 80, and 100 are all multiples of both 4 and 10. 4×10=40 10×4=40 4×15=60 10×6=60 4×20=80 10×8=80 4×25=100 10×10=100

We can find common multiples of more than two numbers as well. Let’s look at 3, 5, and 9:

 3×15=45 5×9=45 9×5=45 45, 90, and 135 are all common multiples of 3, 5 and 9. 3×30=90 5×18=90 9×10=90 3×45=135 5×27=135 9×15=135

Sometimes, we need to determine the Least Common Multiple (LCM) of a set of numbers, in other words, the common multiple that has the lowest value.

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.

Now let’s find the LCM of 4 and 10 by factoring. Remember, factors are numbers that are multiplied together to form a multiple. The LCM of two numbers is the product of the highest power of all prime factors of both numbers. Let’s break that down a bit:

 4=2×2 10=5×2 The prime factor of 4 is 2. The prime factors of 10 are 5 and 2. The factor of 2 occurs twice, so it is represented as 22. So, 4=22. The unique factors here are 2 and 5 and the highest power of 2 is 2, so the LCM equals 22×5=20, just as we determined by making a list.

Now let’s find the LCM of 24, 144, and 48 by factoring:

 24=23×3 144=12×12=24 × 32 48=16×3=24×3 The prime factors of 24 are 2 and 3. The prime factors of 144 are 2 and 3. The prime factors of 48 are 2 and 3. The 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× 32=144. Since 144 is a multiple of both 24 and 48, it is also automatically the LCM of all three numbers.

I hope that this video has increased your understanding of multiples and how they work with numbers!

See you next time!

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by Mometrix Test Preparation | Last Updated: August 19, 2020