LCM for 6, 14 and 18

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What's the Least Common Multiple (LCM) of 6, 14 and 18?

Answer

LCM of 6, 14 and 18 is
126

First common multiples: 126, 252, 378, …

126 is divisible by all three: 126 ÷ 6 = 21, 126 ÷ 14 = 9, 126 ÷ 18 = 7 — and 21, 9 and 7 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/6 by 21 and of y/14 by 9 and of z/18 by 7.

6 = 2 × 3

14 = 2 × 7

18 = 2 × 32

Prime61418Highest power
22222
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 = 2 × 32 × 7 = 126

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LCM Table

1st2nd3rdLCM
361442
461484
5614210
661442
671442
6814168
6914126
61014210
61114462
6121484
61314546
6141442
61415210
61416336
61417714
61418126
61419798
61420420
6142142
61422462
61423966
61424168
614251,050
61426546
61427378
6142884
614291,218
61430210
614311,302
61432672

FAQ

What's the Least Common Multiple (LCM) of 6, 14 and 18?

LCM of 6, 14 and 18 is 126

How to find the LCM of 6, 14 and 18 by prime factorization?

Take every prime that appears in 6, 14 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

Can you get the LCM of 6, 14 and 18 two numbers at a time?

Yes. The LCM of 6 and 14 is 42, and the LCM of 42 and 18 is 126 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 126 divisible by 6, 14 and 18?

Yes, and by definition it is the smallest positive integer that is: 126 ÷ 6, 126 ÷ 14 and 126 ÷ 18 all come out whole. Any other common multiple of 6, 14 and 18 is a multiple of 126.

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