LCM for 16, 20 and 24

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 16, 20 and 24?

Answer

LCM of 16, 20 and 24 is
240

First common multiples: 240, 480, 720, …

240 is divisible by all three: 240 ÷ 16 = 15, 240 ÷ 20 = 12, 240 ÷ 24 = 10 — and 15, 12 and 10 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/16 by 15 and of y/20 by 12 and of z/24 by 10.

16 = 24

20 = 22 × 5

24 = 23 × 3

Prime162024Highest power
224222324
3——33
5—5—5

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

LCM = 24 × 3 × 5 = 240

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LCM Table

1st2nd3rdLCM
91620720
10162080
111620880
121620240
1316201,040
141620560
151620240
16162080
1617201,360
161820720
1619201,520
16202080
1620211,680
162022880
1620231,840
162024240
162025400
1620261,040
1620272,160
162028560
1620292,320
162030240
1620312,480
162032160
1620332,640
1620341,360
162035560
162036720
1620372,960
1620381,520

FAQ

What's the Least Common Multiple (LCM) of 16, 20 and 24?

LCM of 16, 20 and 24 is 240

How to find the LCM of 16, 20 and 24 by prime factorization?

Take every prime that appears in 16, 20 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

Can you get the LCM of 16, 20 and 24 two numbers at a time?

Yes. The LCM of 16 and 20 is 80, and the LCM of 80 and 24 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 240 divisible by 16, 20 and 24?

Yes, and by definition it is the smallest positive integer that is: 240 ÷ 16, 240 ÷ 20 and 240 ÷ 24 all come out whole. Any other common multiple of 16, 20 and 24 is a multiple of 240.

See Also