## What you need to know

Things to remember:

• Common multiples are multiples that are the same for two numbers.
• Multiplying two numbers together gives a common multiple of these two numbers.
• There is an infinite number of multiples, they go on forever!

So, what are multiples of a number? They’re just the times table!

7 times table:

7          14        21        28        35        42        49        56        63        70

Multiples of 7:

7          14        21        28        35        42        49        56        63        70

We can see that these are the same thing!

Now that we know how to find multiples, how can we find common multiples of two numbers? Well, all we do is list the multiples of the two numbers and see if there are any that appear in both!

What are some common multiples of 8 and 18?

We will do this in two steps:

Step 1: Write out some of the multiples of both numbers.

Multiples of 8

8          16        24        32        40        48        56        64        72        80

Multiples of 18

18        36        54        72        90        108      126      144      162      180

If we look at these two lists of multiples, we can see that 72 appears in both lists. So, this means that 72 is a common multiple of 8 and 18.

If we were to keep writing out the multiples of 8, we’d eventually get to the number 144. Notice how 144 is a multiple of 18 as well. More importantly:

$$8\times18=144$$

So, multiplying two numbers together will always make a common multiple!

Find a common multiple 18 and 15:

$$18\times=270$$

270 is a common multiple of 18 and 15.

Find a common multiple of 4 and 6:

$$4\times6=24$$

24 is a common multiple of 4 and 6.

## Example Questions

#### Question 1: What are the first 4 common multiples of 4 and 6?

Multiples of 4

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

Multiples of 6

6          12        18        24        30        36        42        48        54        60

The first 4 common multiples of 4 and 6 are: 12, 24, 36, and 48.

#### Question 2: Find a common multiple of 27 and 25.

$$27\times25=675$$