LCM for 9, 12 and 18

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What's the Least Common Multiple (LCM) of 9, 12 and 18?

Answer

LCM of 9, 12 and 18 is
36

First common multiples: 36, 72, 108, …

36 is divisible by all three: 36 ÷ 9 = 4, 36 ÷ 12 = 3, 36 ÷ 18 = 2 — and 4, 3 and 2 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 4 and of y/12 by 3 and of z/18 by 2.

9 = 32

12 = 22 × 3

18 = 2 × 32

Prime91218Highest power
2—22222
33233232

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

LCM = 22 × 32 = 36

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LCM Table

1st2nd3rdLCM
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
912311,116
91232288

FAQ

What's the Least Common Multiple (LCM) of 9, 12 and 18?

LCM of 9, 12 and 18 is 36

How to find the LCM of 9, 12 and 18 by prime factorization?

Take every prime that appears in 9, 12 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

Can you get the LCM of 9, 12 and 18 two numbers at a time?

Yes. The LCM of 9 and 12 is 36, and the LCM of 36 and 18 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 36 divisible by 9, 12 and 18?

Yes, and by definition it is the smallest positive integer that is: 36 ÷ 9, 36 ÷ 12 and 36 ÷ 18 all come out whole. Any other common multiple of 9, 12 and 18 is a multiple of 36.

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