LCM for 18, 20 and 36

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What's the Least Common Multiple (LCM) of 18, 20 and 36?

Answer

LCM of 18, 20 and 36 is
180

First common multiples: 180, 360, 540, …

180 is divisible by all three: 180 ÷ 18 = 10, 180 ÷ 20 = 9, 180 ÷ 36 = 5 — and 10, 9 and 5 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 10 and of y/20 by 9 and of z/36 by 5.

18 = 2 × 32

20 = 22 × 5

36 = 22 × 32

Prime182036Highest power
22222222
332—3232
5—5—5

— = 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
1820211,260
1820221,980
1820234,140
182024360
182025900
1820262,340
182027540
1820281,260
1820295,220
182030180
1820315,580
1820321,440
1820331,980
1820343,060
1820351,260
182036180
1820376,660
1820383,420
1820392,340
182040360
1820417,380
1820421,260
1820437,740
1820441,980
182045180
1820464,140
1820478,460
182048720
1820498,820
182050900

FAQ

What's the Least Common Multiple (LCM) of 18, 20 and 36?

LCM of 18, 20 and 36 is 180

How to find the LCM of 18, 20 and 36 by prime factorization?

Take every prime that appears in 18, 20 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 18, 20 and 36 two numbers at a time?

Yes. The LCM of 18 and 20 is 180, and the LCM of 180 and 36 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 18, 20 and 36?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 18, 180 ÷ 20 and 180 ÷ 36 all come out whole. Any other common multiple of 18, 20 and 36 is a multiple of 180.

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