LCM for 12, 20 and 32

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What's the Least Common Multiple (LCM) of 12, 20 and 32?

Answer

LCM of 12, 20 and 32 is
480

First common multiples: 480; 960; 1,440; …

480 is divisible by all three: 480 ÷ 12 = 40, 480 ÷ 20 = 24, 480 ÷ 32 = 15 — and 40, 24 and 15 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 40 and of y/20 by 24 and of z/32 by 15.

12 = 22 × 3

20 = 22 × 5

32 = 25

Prime122032Highest power
222222525
33——3
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 = 25 × 3 × 5 = 480

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LCM Table

1st2nd3rdLCM
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
122039780
122040120
1220412,460
122042420
1220432,580
122044660
122045180
1220461,380

FAQ

What's the Least Common Multiple (LCM) of 12, 20 and 32?

LCM of 12, 20 and 32 is 480

How to find the LCM of 12, 20 and 32 by prime factorization?

Take every prime that appears in 12, 20 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 × 5 = 480.

Can you get the LCM of 12, 20 and 32 two numbers at a time?

Yes. The LCM of 12 and 20 is 60, and the LCM of 60 and 32 is 480 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 480 divisible by 12, 20 and 32?

Yes, and by definition it is the smallest positive integer that is: 480 ÷ 12, 480 ÷ 20 and 480 ÷ 32 all come out whole. Any other common multiple of 12, 20 and 32 is a multiple of 480.

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