LCM for 16, 24 and 32

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What's the Least Common Multiple (LCM) of 16, 24 and 32?

Answer

LCM of 16, 24 and 32 is
96

First common multiples: 96, 192, 288, …

96 is divisible by all three: 96 ÷ 16 = 6, 96 ÷ 24 = 4, 96 ÷ 32 = 3 — and 6, 4 and 3 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/16 by 6 and of y/24 by 4 and of z/32 by 3.

16 = 24

24 = 23 × 3

32 = 25

Prime162432Highest power
224232525
3—3—3

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 25 × 3 = 96

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LCM Table

1st2nd3rdLCM
161724816
161824144
161924912
162024240
162124336
162224528
1623241,104
16242448
1624251,200
162426624
162427432
162428336
1624291,392
162430240
1624311,488
16243296
162433528
162434816
1624351,680
162436144
1624371,776
162438912
162439624
162440240
1624411,968
162442336
1624432,064
162444528
162445720
1624461,104

FAQ

What's the Least Common Multiple (LCM) of 16, 24 and 32?

LCM of 16, 24 and 32 is 96

How to find the LCM of 16, 24 and 32 by prime factorization?

Take every prime that appears in 16, 24 and 32 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

Can you get the LCM of 16, 24 and 32 two numbers at a time?

Yes. The LCM of 16 and 24 is 48, and the LCM of 48 and 32 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 96 divisible by 16, 24 and 32?

Yes, and by definition it is the smallest positive integer that is: 96 ÷ 16, 96 ÷ 24 and 96 ÷ 32 all come out whole. Any other common multiple of 16, 24 and 32 is a multiple of 96.

See Also