LCM for 12, 14 and 18

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What's the Least Common Multiple (LCM) of 12, 14 and 18?

Answer

LCM of 12, 14 and 18 is
252

First common multiples: 252, 504, 756, …

252 is divisible by all three: 252 ÷ 12 = 21, 252 ÷ 14 = 18, 252 ÷ 18 = 14 — and 21, 18 and 14 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 21 and of y/14 by 18 and of z/18 by 14.

12 = 22 × 3

14 = 2 × 7

18 = 2 × 32

Prime121418Highest power
2222222
33—3232
7—7—7

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

LCM = 22 × 32 × 7 = 252

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LCM Table

1st2nd3rdLCM
3121484
4121484
51214420
6121484
7121484
81214168
91214252
101214420
111214924
12121484
1213141,092
12141484
121415420
121416336
1214171,428
121418252
1214191,596
121420420
12142184
121422924
1214231,932
121424168
1214252,100
1214261,092
121427756
12142884
1214292,436
121430420
1214312,604
121432672

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 18?

LCM of 12, 14 and 18 is 252

How to find the LCM of 12, 14 and 18 by prime factorization?

Take every prime that appears in 12, 14 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

Can you get the LCM of 12, 14 and 18 two numbers at a time?

Yes. The LCM of 12 and 14 is 84, and the LCM of 84 and 18 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 252 divisible by 12, 14 and 18?

Yes, and by definition it is the smallest positive integer that is: 252 ÷ 12, 252 ÷ 14 and 252 ÷ 18 all come out whole. Any other common multiple of 12, 14 and 18 is a multiple of 252.

See Also