LCM for 3, 5 and 20

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What's the Least Common Multiple (LCM) of 3, 5 and 20?

Answer

LCM of 3, 5 and 20 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 3 = 20, 60 ÷ 5 = 12, 60 ÷ 20 = 3 — and 20, 12 and 3 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/3 by 20 and of y/5 by 12 and of z/20 by 3.

3 — prime

5 — prime

20 = 22 × 5

Prime3520Highest power
2——2222
33——3
5—555

— = 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 = 60

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LCM Table

1st2nd3rdLCM
35515
35630
357105
358120
35945
351030
3511165
351260
3513195
3514210
351515
3516240
3517255
351890
3519285
352060
3521105
3522330
3523345
3524120
352575
3526390
3527135
3528420
3529435
353030
3531465
3532480
3533165
3534510

FAQ

What's the Least Common Multiple (LCM) of 3, 5 and 20?

LCM of 3, 5 and 20 is 60

How to find the LCM of 3, 5 and 20 by prime factorization?

Take every prime that appears in 3, 5 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 3, 5 and 20 two numbers at a time?

Yes. The LCM of 3 and 5 is 15, and the LCM of 15 and 20 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 3, 5 and 20?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 3, 60 ÷ 5 and 60 ÷ 20 all come out whole. Any other common multiple of 3, 5 and 20 is a multiple of 60.

See Also