LCM for 24, 32 and 40

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What's the Least Common Multiple (LCM) of 24, 32 and 40?

Answer

LCM of 24, 32 and 40 is
480

First common multiples: 480; 960; 1,440; …

480 is divisible by all three: 480 ÷ 24 = 20, 480 ÷ 32 = 15, 480 ÷ 40 = 12 — and 20, 15 and 12 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/24 by 20 and of y/32 by 15 and of z/40 by 12.

24 = 23 × 3

32 = 25

40 = 23 × 5

Prime243240Highest power
223252325
33——3
5——55

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

LCM = 25 × 3 × 5 = 480

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LCM Table

1st2nd3rdLCM
2425322,400
2426321,248
242732864
242832672
2429322,784
243032480
2431322,976
24323296
2432331,056
2432341,632
2432353,360
243236288
2432373,552
2432381,824
2432391,248
243240480
2432413,936
243242672
2432434,128
2432441,056
2432451,440
2432462,208
2432474,512
24324896
2432494,704
2432502,400
2432511,632
2432521,248
2432535,088
243254864

FAQ

What's the Least Common Multiple (LCM) of 24, 32 and 40?

LCM of 24, 32 and 40 is 480

How to find the LCM of 24, 32 and 40 by prime factorization?

Take every prime that appears in 24, 32 and 40 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 × 5 = 480.

Can you get the LCM of 24, 32 and 40 two numbers at a time?

Yes. The LCM of 24 and 32 is 96, and the LCM of 96 and 40 is 480 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 480 divisible by 24, 32 and 40?

Yes, and by definition it is the smallest positive integer that is: 480 ÷ 24, 480 ÷ 32 and 480 ÷ 40 all come out whole. Any other common multiple of 24, 32 and 40 is a multiple of 480.

See Also