LESSON: Least Common Multiple

READ: Find the Common Multiples of Different Numbers

Find the Common Multiples of Different Numbers

In mathematics, you have been working with multiples for a long time. One of the first things that you probably learned was how to count by twos or threes. Counting by twos and threes is counting by multiples. When you were small, you didn’t call it “counting by multiples,” but that is exactly what you were doing.

What is a multiple? A multiple is the product of a quantity and a whole number.

What does that mean exactly? It means that when you take a number like 3 that becomes the quantity. Then you multiply that quantity times different whole numbers.

3 $\times$ 2 $=$ 6, 3 $\times$ 3 $=$ 9, 3 $\times$ 4 $=$ 12, 3 $\times$ 5 $=$ 15, 3 $\times$ 6 $=$ 18

Listing out these products is the same as listing out multiples.

3, 6, 9, 12, 15, 18.....

You can see that this is also the same as counting by threes.

The dots at the end mean that these multiples can go on and on and on. Each numbers has an infinite number of multiples.

Example

List five the multiples for 4.

To do this, we can think of taking the quantity 4 and multiplying it by 2, 3, 4, 5, 6.....

4 $\times$ 2 $=$ 8, 4 $\times$ 3 $=$ 12, 4 $\times$ 4 $=$ 16, 4 $\times$ 5 $=$ 20, 4 $\times$ 6 $=$ 24

Our answer is 8, 12, 16, 20, 24.... Notice that we could keep on listing multiples of 4 forever.

What is a common multiple? A common multiple is a multiple that two or more numbers have in common.

Example

What are the common multiples of 3 and 4?

To start to find the common multiples, we first need to write out the multiples for 3 and 4. To find the most common multiples that we can, we can list out multiples through multiplying by 12.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

The common multiples of 3 and 4 are 12, 24, 36.