# 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 = 2^{3 } · 3^{2}

108 = 2^{2 } · 3^{3}

60 = 2^{2 } · 3 · 5

LCM (72, 108, 60) = 2^{3 } · 3^{3} · 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