LCM for 10, 18 and 20

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What's the Least Common Multiple (LCM) of 10, 18 and 20?

Answer

LCM of 10, 18 and 20 is
180

First common multiples: 180, 360, 540, …

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

10 = 2 × 5

18 = 2 × 32

20 = 22 × 5

Prime101820Highest power
2222222
3—32—32
55—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
5101890
6101890
71018630
81018360
9101890
10101890
101118990
101218180
1013181,170
101418630
10151890
101618720
1017181,530
10181890
1018191,710
101820180
101821630
101822990
1018232,070
101824360
101825450
1018261,170
101827270
1018281,260
1018292,610
10183090
1018312,790
1018321,440
101833990
1018341,530

FAQ

What's the Least Common Multiple (LCM) of 10, 18 and 20?

LCM of 10, 18 and 20 is 180

How to find the LCM of 10, 18 and 20 by prime factorization?

Take every prime that appears in 10, 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 10, 18 and 20 two numbers at a time?

Yes. The LCM of 10 and 18 is 90, and the LCM of 90 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 10, 18 and 20?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 10, 180 ÷ 18 and 180 ÷ 20 all come out whole. Any other common multiple of 10, 18 and 20 is a multiple of 180.

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