LCM for 12, 20 and 24

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What's the Least Common Multiple (LCM) of 12, 20 and 24?

Answer

LCM of 12, 20 and 24 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 12 = 10, 120 ÷ 20 = 6, 120 ÷ 24 = 5 — and 10, 6 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/12 by 10 and of y/20 by 6 and of z/24 by 5.

12 = 22 × 3

20 = 22 × 5

24 = 23 × 3

Prime122024Highest power
222222323
33—33
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 = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
91220180
10122060
111220660
12122060
121320780
121420420
12152060
121620240
1217201,020
121820180
1219201,140
12202060
122021420
122022660
1220231,380
122024120
122025300
122026780
122027540
122028420
1220291,740
12203060
1220311,860
122032480
122033660
1220341,020
122035420
122036180
1220372,220
1220381,140

FAQ

What's the Least Common Multiple (LCM) of 12, 20 and 24?

LCM of 12, 20 and 24 is 120

How to find the LCM of 12, 20 and 24 by prime factorization?

Take every prime that appears in 12, 20 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 12, 20 and 24 two numbers at a time?

Yes. The LCM of 12 and 20 is 60, and the LCM of 60 and 24 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 12, 20 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 20 and 120 ÷ 24 all come out whole. Any other common multiple of 12, 20 and 24 is a multiple of 120.

See Also