LCM for 12, 15 and 20

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What's the Least Common Multiple (LCM) of 12, 15 and 20?

Answer

LCM of 12, 15 and 20 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 12 = 5, 60 ÷ 15 = 4, 60 ÷ 20 = 3 — and 5, 4 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/12 by 5 and of y/15 by 4 and of z/20 by 3.

12 = 22 × 3

15 = 3 × 5

20 = 22 × 5

Prime121520Highest power
222—2222
333—3
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
5121560
6121560
71215420
81215120
91215180
10121560
111215660
12121560
121315780
121415420
12151560
121516240
1215171,020
121518180
1215191,140
12152060
121521420
121522660
1215231,380
121524120
121525300
121526780
121527540
121528420
1215291,740
12153060
1215311,860
121532480
121533660
1215341,020

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 20?

LCM of 12, 15 and 20 is 60

How to find the LCM of 12, 15 and 20 by prime factorization?

Take every prime that appears in 12, 15 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 12, 15 and 20 two numbers at a time?

Yes. The LCM of 12 and 15 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 12, 15 and 20?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 12, 60 ÷ 15 and 60 ÷ 20 all come out whole. Any other common multiple of 12, 15 and 20 is a multiple of 60.

See Also