LCM for 12, 30 and 32

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What's the Least Common Multiple (LCM) of 12, 30 and 32?

Answer

LCM of 12, 30 and 32 is
480

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

480 is divisible by all three: 480 ÷ 12 = 40, 480 ÷ 30 = 16, 480 ÷ 32 = 15 — and 40, 16 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/30 by 16 and of z/32 by 15.

12 = 22 × 3

30 = 2 × 3 × 5

32 = 25

Prime123032Highest power
22222525
333—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
1217301,020
121830180
1219301,140
12203060
122130420
122230660
1223301,380
122430120
122530300
122630780
122730540
122830420
1229301,740
12303060
1230311,860
123032480
123033660
1230341,020
123035420
123036180
1230372,220
1230381,140
123039780
123040120
1230412,460
123042420
1230432,580
123044660
123045180
1230461,380

FAQ

What's the Least Common Multiple (LCM) of 12, 30 and 32?

LCM of 12, 30 and 32 is 480

How to find the LCM of 12, 30 and 32 by prime factorization?

Take every prime that appears in 12, 30 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, 30 and 32 two numbers at a time?

Yes. The LCM of 12 and 30 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, 30 and 32?

Yes, and by definition it is the smallest positive integer that is: 480 ÷ 12, 480 ÷ 30 and 480 ÷ 32 all come out whole. Any other common multiple of 12, 30 and 32 is a multiple of 480.

See Also