LCM for 6, 14 and 21

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What's the Least Common Multiple (LCM) of 6, 14 and 21?

Answer

LCM of 6, 14 and 21 is
42

First common multiples: 42, 84, 126, …

42 is divisible by all three: 42 ÷ 6 = 7, 42 ÷ 14 = 3, 42 ÷ 21 = 2 — and 7, 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/6 by 7 and of y/14 by 3 and of z/21 by 2.

6 = 2 × 3

14 = 2 × 7

21 = 3 × 7

Prime61421Highest power
222—2
33—33
7—777

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

LCM = 2 × 3 × 7 = 42

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LCM Table

1st2nd3rdLCM
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
61433462
61434714
61435210

FAQ

What's the Least Common Multiple (LCM) of 6, 14 and 21?

LCM of 6, 14 and 21 is 42

How to find the LCM of 6, 14 and 21 by prime factorization?

Take every prime that appears in 6, 14 and 21 to the highest power it reaches in any one of them and multiply: 2 × 3 × 7 = 42.

Can you get the LCM of 6, 14 and 21 two numbers at a time?

Yes. The LCM of 6 and 14 is 42, and the LCM of 42 and 21 is 42 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 42 divisible by 6, 14 and 21?

Yes, and by definition it is the smallest positive integer that is: 42 ÷ 6, 42 ÷ 14 and 42 ÷ 21 all come out whole. Any other common multiple of 6, 14 and 21 is a multiple of 42.

See Also