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.

Factor Decomposition

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

Factor Decomposition

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

Factor Decomposition

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




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