LCM for 7, 12 and 16

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What's the Least Common Multiple (LCM) of 7, 12 and 16?

Answer

LCM of 7, 12 and 16 is
336

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

336 is divisible by all three: 336 ÷ 7 = 48, 336 ÷ 12 = 28, 336 ÷ 16 = 21 — and 48, 28 and 21 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/7 by 48 and of y/12 by 28 and of z/16 by 21.

7 — prime

12 = 22 × 3

16 = 24

Prime71216Highest power
2—222424
3—3—3
77——7

— = 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
171284
271284
371284
471284
5712420
671284
771284
7812168
7912252
71012420
71112924
7121284
712131,092
7121484
71215420
71216336
712171,428
71218252
712191,596
71220420
7122184
71222924
712231,932
71224168
712252,100
712261,092
71227756
7122884
712292,436
71230420

FAQ

What's the Least Common Multiple (LCM) of 7, 12 and 16?

LCM of 7, 12 and 16 is 336

How to find the LCM of 7, 12 and 16 by prime factorization?

Take every prime that appears in 7, 12 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

Can you get the LCM of 7, 12 and 16 two numbers at a time?

Yes. The LCM of 7 and 12 is 84, and the LCM of 84 and 16 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 7, 12 and 16?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 7, 336 ÷ 12 and 336 ÷ 16 all come out whole. Any other common multiple of 7, 12 and 16 is a multiple of 336.

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