Least Common Multiple

The least common multiple (or LCM) of two or more numbers is the smallest multiple of the numbers, excluding zero.

Calculating the Least Common Multiple

1. Decompose the numbers into prime factors.

2. Select the common factors and the non-common factors with the greatest exponent.

Examples

Find the LCM of: 72, 108 and 60.

72 = 23 · 32

108 = 22 · 33

60 = 22 · 3 · 5

LCM (72, 108, 60) = 23 · 33 · 5 = 2,160

2,160 is the smallest number that can be divided by 72, 108 and 60.

If a number is a multiple of another, then it is the LCM of both.

The number 36 is a multiple of 12.

LCM (12, 36) = 36

Relationship between the GCD and LCM

GCD (a, b) · LCM (a, b) = a · b

GCD (12, 16) = 4

LCM (12, 16) = 48

48 · 4 = 12 ·16

192 = 192