LCM for 12, 15 and 18

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What's the Least Common Multiple (LCM) of 12, 15 and 18?

Answer

LCM of 12, 15 and 18 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 12 = 15, 180 ÷ 15 = 12, 180 ÷ 18 = 10 — and 15, 12 and 10 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 15 and of y/15 by 12 and of z/18 by 10.

12 = 22 × 3

15 = 3 × 5

18 = 2 × 32

Prime121518Highest power
222—222
3333232
5—5—5

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

LCM = 22 × 32 × 5 = 180

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LCM Table

1st2nd3rdLCM
3121560
4121560
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

FAQ

What's the Least Common Multiple (LCM) of 12, 15 and 18?

LCM of 12, 15 and 18 is 180

How to find the LCM of 12, 15 and 18 by prime factorization?

Take every prime that appears in 12, 15 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 12, 15 and 18 two numbers at a time?

Yes. The LCM of 12 and 15 is 60, and the LCM of 60 and 18 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 12, 15 and 18?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 15 and 180 ÷ 18 all come out whole. Any other common multiple of 12, 15 and 18 is a multiple of 180.

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