LCM for 18, 21 and 36

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What's the Least Common Multiple (LCM) of 18, 21 and 36?

Answer

LCM of 18, 21 and 36 is
252

First common multiples: 252, 504, 756, …

252 is divisible by all three: 252 ÷ 18 = 14, 252 ÷ 21 = 12, 252 ÷ 36 = 7 — and 14, 12 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/18 by 14 and of y/21 by 12 and of z/36 by 7.

18 = 2 × 32

21 = 3 × 7

36 = 22 × 32

Prime182136Highest power
22—2222
33233232
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
182121126
1821221,386
1821232,898
182124504
1821253,150
1821261,638
182127378
182128252
1821293,654
182130630
1821313,906
1821322,016
1821331,386
1821342,142
182135630
182136252
1821374,662
1821382,394
1821391,638
1821402,520
1821415,166
182142126
1821435,418
1821442,772
182145630
1821462,898
1821475,922
1821481,008
182149882
1821503,150

FAQ

What's the Least Common Multiple (LCM) of 18, 21 and 36?

LCM of 18, 21 and 36 is 252

How to find the LCM of 18, 21 and 36 by prime factorization?

Take every prime that appears in 18, 21 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

Can you get the LCM of 18, 21 and 36 two numbers at a time?

Yes. The LCM of 18 and 21 is 126, and the LCM of 126 and 36 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 18, 21 and 36?

Yes, and by definition it is the smallest positive integer that is: 252 ÷ 18, 252 ÷ 21 and 252 ÷ 36 all come out whole. Any other common multiple of 18, 21 and 36 is a multiple of 252.

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