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Calculate the Least Common Multiple or LCM of 45, 54 and 72

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The instructions to find the LCM of 45, 54 and 72 are the next:

1. Decompose all numbers into prime factors

453
153
55
1
542
273
93
33
1
722
362
182
93
33
1

2. Write all numbers as the product of its prime factors

Prime factors of 45=32 . 5
Prime factors of 54=2 . 33
Prime factors of 72=23 . 32

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 3

Common prime factors with the greatest exponent: 33

Uncommon prime factors: 5 , 2

Uncommon prime factors with the greatest exponent: 51, 23

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 33. 51. 23 = 1080


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