Hello, and welcome to this video about multiples! In this video, we’ll take a look at:
- What is a multiple in math?
- Common multiples
- Least common multiples
Examples of 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:
Some numbers are multiples of many different numbers. Take 12 for example:
Other numbers are only multiples of 2 numbers, for example, 7:
Now that we know what multiples are, here are a couple of truths to remember about them:
- Zero is a multiple of all numbers. For any number
a a×0=0 - Every number is a multiple of 1 and itself. For any number
a a×1=a
Common Multiple
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:
We can find common multiples of more than two numbers as well. Let’s look at 3, 5, and 9:
Least Common Multiple
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 factor of both numbers. Let’s break that down a bit:
| 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
Now let’s find the LCM of 24, 144, and 48 by factoring:
| 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
I hope that this video has increased your understanding of multiples and how they work with numbers!
See you next time!
Frequently Asked Questions
Q
What are multiples and factors?
A
Factors and multiples are very closely related. Factors are the numbers we can multiply together in order to get another number. The number that is created by multiplying these factors is called a multiple. Multiples can be found by multiplying factors, or simply by skip counting. For example, the multiples of
Q
What is the difference between a factor and a multiple?
A
Factors are the numbers that are multiplied in order to create a multiple. Multiples are the numbers created by multiplying two factors. Multiples are unlimited, and can be found by simply skip counting. For example, the multiples of
Q
What is a multiple in math?
A
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,
Q
How do you calculate multiples?
A
Multiples can be found simply by skip counting. For example, the multiples of
Q
Why are factors and multiples important?
A
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. For example, when simplifying the fraction
Q
What is the definition of a factor in math?
A
Factors are the numbers we can multiply together in order to get another number. For example, the factors of
Q
What does it mean to be a multiple?
A
In order for a number to be considered a multiple, it needs to be the result of multiplying a number and an integer. An integer is simply a whole number that is not a fraction. For example,
What is a Multiple? (PDF)
Multiple Practice Questions
Which list shows values that are all multiples of 4?
Determine the LCM of 42 and 126.
What is the LCM of 3, 5 and 8?
Zoe has a watering schedule for her two plants. She waters her cacti every 10 days and her lilies every 3 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?
Marcus swims every 3rd 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?
