LCM for 10, 15 and 20

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What's the Least Common Multiple (LCM) of 10, 15 and 20?

Answer

LCM of 10, 15 and 20 is
60

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 10 = 6, 60 ÷ 15 = 4, 60 ÷ 20 = 3 — and 6, 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/10 by 6 and of y/15 by 4 and of z/20 by 3.

10 = 2 × 5

15 = 3 × 5

20 = 22 × 5

Prime101520Highest power
22—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
5101530
6101530
71015210
81015120
9101590
10101530
101115330
10121560
101315390
101415210
10151530
101516240
101517510
10151890
101519570
10152060
101521210
101522330
101523690
101524120
101525150
101526390
101527270
101528420
101529870
10153030
101531930
101532480
101533330
101534510

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 20?

LCM of 10, 15 and 20 is 60

How to find the LCM of 10, 15 and 20 by prime factorization?

Take every prime that appears in 10, 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 10, 15 and 20 two numbers at a time?

Yes. The LCM of 10 and 15 is 30, and the LCM of 30 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 10, 15 and 20?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 10, 60 ÷ 15 and 60 ÷ 20 all come out whole. Any other common multiple of 10, 15 and 20 is a multiple of 60.

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