# What is a Multiple in Math?

Understanding multiples can help your student find patterns, solve equations, and strengthen their multiplication and division skills.

Author
Katie Wickliff

Published
November 8, 2023

# What is a Multiple in Math?

Understanding multiples can help your student find patterns, solve equations, and strengthen their multiplication and division skills.

Author
Katie Wickliff

Published
Nov 8, 2023

# What is a Multiple in Math?

Understanding multiples can help your student find patterns, solve equations, and strengthen their multiplication and division skills.

Author
Katie Wickliff

Published
Nov 8, 2023

Key takeaways

• Multiples are the numbers you get when you multiply other numbers together.
• Many numbers have an unlimited number of multiples, but some numbers have only a few.
• Being able to find common multiples is an essential part of working with fractions.

Understanding the concept of multiples is key to mastering multiplication. In this article, we’ll explain what multiples are and provide examples of the multiples of 3 through 12. To help your student practice multiples, we’ve included a set of problems with a parent guide.

## What are multiples?

In math, multiples are the numbers you get when you multiply other numbers together. For example, when we multiply 2×5, our answer (also called the product) is 10. So, 10 is a multiple of 2 and also a multiple of 5.

## Important Properties of Multiples

Besides 0, the rest of the natural numbers have an infinite number of multiples.

Every multiple of a number is larger or equal to that number.

Every number is a multiple of itself.

Every number is a multiple of

Some numbers are a multiple of themselves and 1. These are called prime numbers.

Using the repeated subtraction process as a foundation can help students gain the confidence to tackle more complex division problems with varying strategies, such as short or long division.

## Multiples Examples/List

Below are the first several multiples of numbers. As we know, many numbers have an infinite number of multiples.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 120

## Common Multiples

Common multiples are the multiples that two or more numbers share. When working with fractions, a student will often need to know common multiples and be able to find the least common multiple. For example, let’s look at the multiples of numbers 3 and 9.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

The multiples that both 3 and 9 have in common are: 9, 18, and 27. Note: 3 and 9 have more common multiples, but these are the first few.

## Practice Problems for Multiples in Math

Now that you understand multiples, demonstrate your knowledge by completing these five problems. For even more practice, head over to DoodleLearning’s award-winning math appScroll down the page for the answers!

The first three multiples of the number 9 are:

1. 1, 9, 18
2. 1, 3, 9
3. 0, 9, 18
4. 9, 18, 27

I am the least common multiple of the numbers 6 and 12. What number am I?

Fill in the blanks with the first five multiples of the number 4.

4, ____, ____, _____, _____, ____

The number of stuffed animals in Ella’s collection is a 2-digit number that is divisible by 6 and a multiple of 4. She has less than 30 stuffed animals but more than 15 in her collection. How many stuffed animals does Ella have? Show your thinking.

Which of the following numbers is not a common multiple of 8 and 10? Circle all that apply.

1. 8
2. 40
3. 24
4. 80

D

12

8, 12, 16, 20, 24

24

First, list out the multiples of 4 that are less than 30: 4, 8, 12, 16, 20, 24, 28

Next, find the multiples that are divisible by 6: 12,  24

If Ella has more than 15 animals in her collection, the answer must be 24.

A, C are not common multiples of both 8 and 10

A multiple in math is the number you get when you multiply other numbers together.

The least common multiple is the smallest multiple two (or more) numbers have in common. For example, to find the least common multiple of 4 and 6, you’d compare their multiples:

Multiples of 4: 4, 8, 12, 16, 20….

Multiples of 6: 6, 12, 18, 24, 30….

The smallest number both 4 and 6 have in common is 12, so 12 is the least common multiple.

Factors and multiples are closely related: factors are the numbers that can be multiplied together. A multiple is the product of multiplying factors together.

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

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