Lowest Common Multiple

Lowest Common Multiple

GCSE(F) GCSE(H)

Multiples can be shared by numbers. The lowest multiple shared by two numbers is called the Lowest Common Multiple, or LCM.

multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, ...

multiples of 12 are: 12, 24, 36, 48, 60, 72, ...

Multiples that appear in both lists are 36 and 72. The Lowest Common Multiple is 36, which is the first multiple that 9 and 12 share.

For larger numbers, it is easier to determine the LCM by using the product of the primes for each number.

Using a Venn Diagram, the union of the two sets represents the lowest common multiple. Higher Students: This can be written as for example) 9 ∪ 12, or 9 union 12.

Examples

1. What is the LCM of 8 and 10?

Answer: 40

By inspection:

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

Factors of 10: 10, 20, 30, 40, 50, 60

The lowest common multiple is 40.

2. In a game, one type of alien appears ever 22 seconds. A second type of alien appears every 36 seconds. If they have just appeared together, how long will it be until they appear together again?

Answer: 198 seconds

This is a Lowest Common Multiple question. Using prime factors:

22: 2 x 11

36: 2 x 2 x 3 x 3

LCM = 2 x 2 x 3 x 3 x 11 = 396.

Venn Diagram for LCM of 22 and 36