LCM for 5, 12 and 20

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What's the Least Common Multiple (LCM) of 5, 12 and 20?

Answer

LCM of 5, 12 and 20 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 5 = 12, 60 ÷ 12 = 5, 60 ÷ 20 = 3 — and 12, 5 and 3 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/5 by 12 and of y/12 by 5 and of z/20 by 3.

5 — prime

12 = 22 × 3

20 = 22 × 5

Prime51220Highest power
2—222222
3—3—3
55—55

— = 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 = 60

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LCM Table

1st2nd3rdLCM
551260
561260
5712420
5812120
5912180
5101260
51112660
5121260
51213780
51214420
5121560
51216240
512171,020
51218180
512191,140
5122060
51221420
51222660
512231,380
51224120
51225300
51226780
51227540
51228420
512291,740
5123060
512311,860
51232480
51233660
512341,020

FAQ

What's the Least Common Multiple (LCM) of 5, 12 and 20?

LCM of 5, 12 and 20 is 60

How to find the LCM of 5, 12 and 20 by prime factorization?

Take every prime that appears in 5, 12 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 5, 12 and 20 two numbers at a time?

Yes. The LCM of 5 and 12 is 60, and the LCM of 60 and 20 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 5, 12 and 20?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 5, 60 ÷ 12 and 60 ÷ 20 all come out whole. Any other common multiple of 5, 12 and 20 is a multiple of 60.

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