# LCM

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

### Steps to Calculate the LCM

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

Calculate the lowest common multiple (LCM) of the following numbers:

1. 1,048, 7,86 and 3,930

1,048 = 23 · 131

786 = 2 · 3 · 131

3,930 = 2 · 3 · 5 · 131

GCD (1,048, 786, 3,930) = 2 · 131 = 262

LCM (1,048, 786, 3,930) = 23 · 3 · 5 · 131 = 15,720

2. 3,120, 6,200 and 1,864

3,210 = 24 · 3 · 5 · 13

6,200 = 23 · 52 · 31

1,864 = 23 · 233

GCD (3,210, 6,200, 1,864) = 23 = 8

LCM (3,210, 6,200, 1,864) = 24 ·3 · 52 · 13 · 31 · 233 =

= 1,746,521,400