LCM for 12, 14 and 20

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What's the Least Common Multiple (LCM) of 12, 14 and 20?

Answer

LCM of 12, 14 and 20 is
420

First common multiples: 420; 840; 1,260; …

420 is divisible by all three: 420 ÷ 12 = 35, 420 ÷ 14 = 30, 420 ÷ 20 = 21 — and 35, 30 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 35 and of y/14 by 30 and of z/20 by 21.

12 = 22 × 3

14 = 2 × 7

20 = 22 × 5

Prime121420Highest power
22222222
33——3
5——55
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 = 22 × 3 × 5 × 7 = 420

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LCM Table

1st2nd3rdLCM
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
1214312,604
121432672
121433924
1214341,428

FAQ

What's the Least Common Multiple (LCM) of 12, 14 and 20?

LCM of 12, 14 and 20 is 420

How to find the LCM of 12, 14 and 20 by prime factorization?

Take every prime that appears in 12, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 12, 14 and 20 two numbers at a time?

Yes. The LCM of 12 and 14 is 84, and the LCM of 84 and 20 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 12, 14 and 20?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 14 and 420 ÷ 20 all come out whole. Any other common multiple of 12, 14 and 20 is a multiple of 420.

See Also