What is the LCM of 84 and 420?

What's the Least Common Multiple (LCM) of 84 and 420?

Answer

LCM of 84 and 420 is

420

First common multiples: 420; 840; 1,260; …

As a common denominator: multiply the top and bottom of x/84 by 5.

84 divides 420 (420 ÷ 84 = 5), so the LCM is the larger number itself.

84 = 2² × 3 × 7

420 = 2² × 3 × 5 × 7

Prime	84	420	Highest power
2	2²	2²	2²
3	3	3	3
5	—	5	5
7	7	7	7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2² × 3 × 5 × 7 = 420

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