LCM for 6, 11 and 18

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What's the Least Common Multiple (LCM) of 6, 11 and 18?

Answer

LCM of 6, 11 and 18 is
198

First common multiples: 198, 396, 594, …

198 is divisible by all three: 198 ÷ 6 = 33, 198 ÷ 11 = 18, 198 ÷ 18 = 11 — and 33, 18 and 11 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 33 and of y/11 by 18 and of z/18 by 11.

6 = 2 × 3

11 — prime

18 = 2 × 32

Prime61118Highest power
22—22
33—3232
11—11—11

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

LCM = 2 × 32 × 11 = 198

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LCM Table

1st2nd3rdLCM
361166
4611132
5611330
661166
6711462
6811264
6911198
61011330
6111166
61112132
61113858
61114462
61115330
61116528
611171,122
61118198
611191,254
61120660
61121462
6112266
611231,518
61124264
611251,650
61126858
61127594
61128924
611291,914
61130330
611312,046
611321,056

FAQ

What's the Least Common Multiple (LCM) of 6, 11 and 18?

LCM of 6, 11 and 18 is 198

How to find the LCM of 6, 11 and 18 by prime factorization?

Take every prime that appears in 6, 11 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 11 = 198.

Can you get the LCM of 6, 11 and 18 two numbers at a time?

Yes. The LCM of 6 and 11 is 66, and the LCM of 66 and 18 is 198 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 198 divisible by 6, 11 and 18?

Yes, and by definition it is the smallest positive integer that is: 198 ÷ 6, 198 ÷ 11 and 198 ÷ 18 all come out whole. Any other common multiple of 6, 11 and 18 is a multiple of 198.

See Also