LCM for 15, 20 and 24

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What's the Least Common Multiple (LCM) of 15, 20 and 24?

Answer

LCM of 15, 20 and 24 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 15 = 8, 120 ÷ 20 = 6, 120 ÷ 24 = 5 — and 8, 6 and 5 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/15 by 8 and of y/20 by 6 and of z/24 by 5.

15 = 3 × 5

20 = 22 × 5

24 = 23 × 3

Prime152024Highest power
2—222323
33—33
555—5

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
91520180
10152060
111520660
12152060
131520780
141520420
15152060
151620240
1517201,020
151820180
1519201,140
15202060
152021420
152022660
1520231,380
152024120
152025300
152026780
152027540
152028420
1520291,740
15203060
1520311,860
152032480
152033660
1520341,020
152035420
152036180
1520372,220
1520381,140

FAQ

What's the Least Common Multiple (LCM) of 15, 20 and 24?

LCM of 15, 20 and 24 is 120

How to find the LCM of 15, 20 and 24 by prime factorization?

Take every prime that appears in 15, 20 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 15, 20 and 24 two numbers at a time?

Yes. The LCM of 15 and 20 is 60, and the LCM of 60 and 24 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 15, 20 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 15, 120 ÷ 20 and 120 ÷ 24 all come out whole. Any other common multiple of 15, 20 and 24 is a multiple of 120.

See Also