1
### Meaning

30, 60, 90 are all common multiples of 6, 10 and 15. 30 is the lowest number that 6, 10 and 15 will divide into. We say that 30 is the lowest common multiple of 6, 10 and 15.

2

LCM is short for lowest common multiple. The LCM of 4, 5 and 6 is 60 (not 120).

3
### Steps

To find the LCM of a set of numbers:
a) express the numbers as a product of prime factors;
b) find the lowest product of factors which contains all of the prime factors of the numbers.

4
### Example 1

Find the LCM of 8, 9 and 12.
8 = 2 x 2 x 2
Any multiple of 8 must contain 2 x 2 x 2.
9 = 3 x 3
Any multiple of 9 must contain 3 x 3.
12 = 2 x 2 x 3
Any multiple of 12 must contain 2 x 2 x 3.
The lowest product containing all three is 2 x 2 x 2 x 3 x 3
The LCM of 8,9 and 12 is
2 x 2 x 2 x 3 x 3 = 72

5
### Example 2

Find the LCM of 24, 28, 36 and 50.
In indices 24 = 23 x 3
28 = 22 X 7
36 = 22 X 32
50 = 2 X 52
The LCM= 23 X Y X 52 X 7 = 12600.
Note: The prime factors are 2,3,5 and 7. The LCM contains the highest powers of 2, 3, 5 and 7 that appear in the factorised numbers

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