LCM for 24, 36 and 40

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What's the Least Common Multiple (LCM) of 24, 36 and 40?

Answer

LCM of 24, 36 and 40 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 24 = 15, 360 ÷ 36 = 10, 360 ÷ 40 = 9 — and 15, 10 and 9 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 15 and of y/36 by 10 and of z/40 by 9.

24 = 23 × 3

36 = 22 × 32

40 = 23 × 5

Prime243640Highest power
223222323
3332—32
5——55

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

LCM = 23 × 32 × 5 = 360

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LCM Table

1st2nd3rdLCM
2425361,800
242636936
242736216
242836504
2429362,088
243036360
2431362,232
243236288
243336792
2434361,224
2435362,520
24363672
2436372,664
2436381,368
243639936
243640360
2436412,952
243642504
2436433,096
243644792
243645360
2436461,656
2436473,384
243648144
2436493,528
2436501,800
2436511,224
243652936
2436533,816
243654216

FAQ

What's the Least Common Multiple (LCM) of 24, 36 and 40?

LCM of 24, 36 and 40 is 360

How to find the LCM of 24, 36 and 40 by prime factorization?

Take every prime that appears in 24, 36 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 24, 36 and 40 two numbers at a time?

Yes. The LCM of 24 and 36 is 72, and the LCM of 72 and 40 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 24, 36 and 40?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 24, 360 ÷ 36 and 360 ÷ 40 all come out whole. Any other common multiple of 24, 36 and 40 is a multiple of 360.

See Also