LCM for 4, 14 and 20

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What's the Least Common Multiple (LCM) of 4, 14 and 20?

Answer

LCM of 4, 14 and 20 is
140

First common multiples: 140, 280, 420, …

140 is divisible by all three: 140 ÷ 4 = 35, 140 ÷ 14 = 10, 140 ÷ 20 = 7 — and 35, 10 and 7 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/4 by 35 and of y/14 by 10 and of z/20 by 7.

4 = 22

14 = 2 × 7

20 = 22 × 5

Prime41420Highest power
22222222
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 × 5 × 7 = 140

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LCM Table

1st2nd3rdLCM
4514140
461484
471428
481456
4914252
41014140
41114308
4121484
41314364
4141428
41415420
41416112
41417476
41418252
41419532
41420140
4142184
41422308
41423644
41424168
41425700
41426364
41427756
4142828
41429812
41430420
41431868
41432224
41433924
41434476

FAQ

What's the Least Common Multiple (LCM) of 4, 14 and 20?

LCM of 4, 14 and 20 is 140

How to find the LCM of 4, 14 and 20 by prime factorization?

Take every prime that appears in 4, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

Can you get the LCM of 4, 14 and 20 two numbers at a time?

Yes. The LCM of 4 and 14 is 28, and the LCM of 28 and 20 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 140 divisible by 4, 14 and 20?

Yes, and by definition it is the smallest positive integer that is: 140 ÷ 4, 140 ÷ 14 and 140 ÷ 20 all come out whole. Any other common multiple of 4, 14 and 20 is a multiple of 140.

See Also