LCM for 12, 14 and 16

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What's the Least Common Multiple (LCM) of 12, 14 and 16?

Answer

LCM of 12, 14 and 16 is
336

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

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

12 = 22 × 3

14 = 2 × 7

16 = 24

Prime121416Highest power
22222424
33——3
7—7—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
1121484
2121484
3121484
4121484
51214420
6121484
7121484
81214168
91214252
101214420
111214924
12121484
1213141,092
12141484
121415420
121416336
1214171,428
121418252
1214191,596
121420420
12142184
121422924
1214231,932
121424168
1214252,100
1214261,092
121427756
12142884
1214292,436
121430420

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 16?

LCM of 12, 14 and 16 is 336

How to find the LCM of 12, 14 and 16 by prime factorization?

Take every prime that appears in 12, 14 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 12, 14 and 16 two numbers at a time?

Yes. The LCM of 12 and 14 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 12, 14 and 16?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 12, 336 ÷ 14 and 336 ÷ 16 all come out whole. Any other common multiple of 12, 14 and 16 is a multiple of 336.

See Also