Year 8 Interactive Maths - Second Edition

## Multiples

The multiples of a number are its products with the natural numbers 1, 2, 3, 4, 5, ....

So, the multiples of 8 are 8, 16, 24, 32, and so on.

###### Note:

The multiples of a number are obtained by multiplying the number by each of the natural numbers.

#### Example 13

Write down the first five multiples of 9.

##### Solution:

The multiples of 9 are obtained by multiplying 9 with the natural numbers 1, 2, 3, 4, 5 …

So, the first five multiples of 9 are 9, 18, 27, 36 and 45.

### Common Multiples

Common multiples are multiples that are common to two or more numbers.

E.g.  Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, …
Multiples of 3 are 3, 6, 9, 12, 15, 18, …

So, common multiples of 2 and 3 are 6, 12, 18, …

#### Example 14

Find the common multiples of 3 and 4.

##### Solution:

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, …
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, …

So, the common multiples of 3 and 4 are 12, 24, 36, …

### Lowest Common Multiple

The lowest common multiple (LCM) of two or more numbers is the smallest common multiple.

E.g.  Multiples of 8 are 8, 16, 24, 32, …
Multiples of 6 are 6, 12, 18, 24, …

###### In general:

To find the lowest common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number.  This is the LCM.

#### Example 15

Find the lowest common multiple of 2 and 5.

##### Solution:

List the multiples of 5 and stop when you find a multiple of 2.

Multiples of 5 are 5, 10, …
Multiples of 2 are 2, 4, 6, 8, 10, …