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Multiples
The multiples of a number are its products with the natural numbers 1, 2, 3, 4, 5, ....
Example 1
1 x 8 = 8
2 x 8 =16
3 x 8 =24
4 x 8 =32
5 x 8 =40
So, the multiples of 8 are 8, 16, 24, 32, 40 and so on.
Note:
The multiples of a number are obtained by multiplying the number by each of the natural numbers.

Example 2
Write down the first five multiples of 9.
Solution:
1 x 9 = 9
2 x 9 =18
3 x 9 =27
4 x 9 =36
5 x 9 =45
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.

Example 3
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 4
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.
Example 5
Multiples of 8 are 8, 16, 24, 32, …
Multiples of 6 are 6, 12, 18, 24, …
The LCM of 6 and 8 is 24
.
Example 6
Find the lowest common multiple of 2 and 5.
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, …
The LCM of 2 and 5 is 10