LCM for 5, 15 and 20

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What's the Least Common Multiple (LCM) of 5, 15 and 20?

Answer

LCM of 5, 15 and 20 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 5 = 12, 60 ÷ 15 = 4, 60 ÷ 20 = 3 — and 12, 4 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/5 by 12 and of y/15 by 4 and of z/20 by 3.

5 — prime

15 = 3 × 5

20 = 22 × 5

Prime51520Highest power
2——2222
3—3—3
55555

— = 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
551515
561530
5715105
5815120
591545
5101530
51115165
5121560
51315195
51415210
5151515
51516240
51517255
5151890
51519285
5152060
51521105
51522330
51523345
51524120
5152575
51526390
51527135
51528420
51529435
5153030
51531465
51532480
51533165
51534510

FAQ

What's the Least Common Multiple (LCM) of 5, 15 and 20?

LCM of 5, 15 and 20 is 60

How to find the LCM of 5, 15 and 20 by prime factorization?

Take every prime that appears in 5, 15 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 5, 15 and 20 two numbers at a time?

Yes. The LCM of 5 and 15 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 5, 15 and 20?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 5, 60 ÷ 15 and 60 ÷ 20 all come out whole. Any other common multiple of 5, 15 and 20 is a multiple of 60.

See Also