LCM for 5, 20 and 30

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What's the Least Common Multiple (LCM) of 5, 20 and 30?

Answer

LCM of 5, 20 and 30 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 5 = 12, 60 ÷ 20 = 3, 60 ÷ 30 = 2 — and 12, 3 and 2 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/20 by 3 and of z/30 by 2.

5 — prime

20 = 22 × 5

30 = 2 × 3 × 5

Prime52030Highest power
2—22222
3——33
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
5152060
5162080
51720340
51820180
51920380
5202020
52021420
52022220
52023460
52024120
52025100
52026260
52027540
52028140
52029580
5203060
52031620
52032160
52033660
52034340
52035140
52036180
52037740
52038380
52039780
5204040
52041820
52042420
52043860
52044220

FAQ

What's the Least Common Multiple (LCM) of 5, 20 and 30?

LCM of 5, 20 and 30 is 60

How to find the LCM of 5, 20 and 30 by prime factorization?

Take every prime that appears in 5, 20 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 5, 20 and 30 two numbers at a time?

Yes. The LCM of 5 and 20 is 20, and the LCM of 20 and 30 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, 20 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 5, 60 ÷ 20 and 60 ÷ 30 all come out whole. Any other common multiple of 5, 20 and 30 is a multiple of 60.

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