LCM for 16, 24 and 28

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What's the Least Common Multiple (LCM) of 16, 24 and 28?

Answer

LCM of 16, 24 and 28 is
336

First common multiples: 336; 672; 1,008; …

336 is divisible by all three: 336 ÷ 16 = 21, 336 ÷ 24 = 14, 336 ÷ 28 = 12 — and 21, 14 and 12 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 21 and of y/24 by 14 and of z/28 by 12.

16 = 24

24 = 23 × 3

28 = 22 × 7

Prime162428Highest power
224232224
3—3—3
7——77

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

LCM = 24 × 3 × 7 = 336

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LCM Table

1st2nd3rdLCM
131624624
141624336
151624240
16162448
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

FAQ

What's the Least Common Multiple (LCM) of 16, 24 and 28?

LCM of 16, 24 and 28 is 336

How to find the LCM of 16, 24 and 28 by prime factorization?

Take every prime that appears in 16, 24 and 28 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

Can you get the LCM of 16, 24 and 28 two numbers at a time?

Yes. The LCM of 16 and 24 is 48, and the LCM of 48 and 28 is 336 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 336 divisible by 16, 24 and 28?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 16, 336 ÷ 24 and 336 ÷ 28 all come out whole. Any other common multiple of 16, 24 and 28 is a multiple of 336.

See Also