LCM for 12, 18 and 20

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What's the Least Common Multiple (LCM) of 12, 18 and 20?

Answer

LCM of 12, 18 and 20 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 12 = 15, 180 ÷ 18 = 10, 180 ÷ 20 = 9 — and 15, 10 and 9 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 15 and of y/18 by 10 and of z/20 by 9.

12 = 22 × 3

18 = 2 × 32

20 = 22 × 5

Prime121820Highest power
22222222
3332—32
5——55

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

LCM = 22 × 32 × 5 = 180

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LCM Table

1st2nd3rdLCM
51218180
6121836
71218252
8121872
9121836
101218180
111218396
12121836
121318468
121418252
121518180
121618144
121718612
12181836
121819684
121820180
121821252
121822396
121823828
12182472
121825900
121826468
121827108
121828252
1218291,044
121830180
1218311,116
121832288
121833396
121834612

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 20?

LCM of 12, 18 and 20 is 180

How to find the LCM of 12, 18 and 20 by prime factorization?

Take every prime that appears in 12, 18 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 12, 18 and 20 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 20 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 12, 18 and 20?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 18 and 180 ÷ 20 all come out whole. Any other common multiple of 12, 18 and 20 is a multiple of 180.

See Also