LCM for 9, 12 and 15

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What's the Least Common Multiple (LCM) of 9, 12 and 15?

Answer

LCM of 9, 12 and 15 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 9 = 20, 180 ÷ 12 = 15, 180 ÷ 15 = 12 — and 20, 15 and 12 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/9 by 20 and of y/12 by 15 and of z/15 by 12.

9 = 32

12 = 22 × 3

15 = 3 × 5

Prime91215Highest power
2—22—22
3323332
5——55

— = 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
191236
291236
391236
491236
5912180
691236
7912252
891272
991236
91012180
91112396
9121236
91213468
91214252
91215180
91216144
91217612
9121836
91219684
91220180
91221252
91222396
91223828
9122472
91225900
91226468
91227108
91228252
912291,044
91230180

FAQ

What's the Least Common Multiple (LCM) of 9, 12 and 15?

LCM of 9, 12 and 15 is 180

How to find the LCM of 9, 12 and 15 by prime factorization?

Take every prime that appears in 9, 12 and 15 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 9, 12 and 15 two numbers at a time?

Yes. The LCM of 9 and 12 is 36, and the LCM of 36 and 15 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 9, 12 and 15?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 9, 180 ÷ 12 and 180 ÷ 15 all come out whole. Any other common multiple of 9, 12 and 15 is a multiple of 180.

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