LCM for 12, 15 and 60

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What's the Least Common Multiple (LCM) of 12, 15 and 60?

Answer

LCM of 12, 15 and 60 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 12 = 5, 60 ÷ 15 = 4, 60 ÷ 60 = 1 — and 5, 4 and 1 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/12 by 5 and of y/15 by 4.

12 = 22 × 3

15 = 3 × 5

60 = 22 × 3 × 5

Prime121560Highest power
222—2222
33333
5—555

— = 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
121545180
1215461,380
1215472,820
121548240
1215492,940
121550300
1215511,020
121552780
1215533,180
121554540
121555660
121556840
1215571,140
1215581,740
1215593,540
12156060
1215613,660
1215621,860
1215631,260
121564960
121565780
121566660
1215674,020
1215681,020
1215691,380
121570420
1215714,260
121572360
1215734,380
1215742,220

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 60?

LCM of 12, 15 and 60 is 60

How to find the LCM of 12, 15 and 60 by prime factorization?

Take every prime that appears in 12, 15 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 12, 15 and 60 two numbers at a time?

Yes. The LCM of 12 and 15 is 60, and the LCM of 60 and 60 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 12, 15 and 60?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 12, 60 ÷ 15 and 60 ÷ 60 all come out whole. Any other common multiple of 12, 15 and 60 is a multiple of 60.

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