LCM for 5, 12 and 15

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What's the Least Common Multiple (LCM) of 5, 12 and 15?

Answer

LCM of 5, 12 and 15 is
60

First common multiples: 60, 120, 180, …

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

5 — prime

12 = 22 × 3

15 = 3 × 5

Prime51215Highest power
2—22—22
3—333
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
151260
251260
351260
451260
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

FAQ

What's the Least Common Multiple (LCM) of 5, 12 and 15?

LCM of 5, 12 and 15 is 60

How to find the LCM of 5, 12 and 15 by prime factorization?

Take every prime that appears in 5, 12 and 15 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 15 two numbers at a time?

Yes. The LCM of 5 and 12 is 60, and the LCM of 60 and 15 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 15?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 5, 60 ÷ 12 and 60 ÷ 15 all come out whole. Any other common multiple of 5, 12 and 15 is a multiple of 60.

See Also