LCM for 8, 24 and 40

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What's the Least Common Multiple (LCM) of 8, 24 and 40?

Answer

LCM of 8, 24 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 24 = 5, 120 ÷ 40 = 3 — and 15, 5 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/8 by 15 and of y/24 by 5 and of z/40 by 3.

8 = 23

24 = 23 × 3

40 = 23 × 5

Prime82440Highest power
223232323
3—3—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 = 23 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
82425600
82426312
82427216
82428168
82429696
82430120
82431744
8243296
82433264
82434408
82435840
8243672
82437888
82438456
82439312
82440120
82441984
82442168
824431,032
82444264
82445360
82446552
824471,128
8244848
824491,176
82450600
82451408
82452312
824531,272
82454216

FAQ

What's the Least Common Multiple (LCM) of 8, 24 and 40?

LCM of 8, 24 and 40 is 120

How to find the LCM of 8, 24 and 40 by prime factorization?

Take every prime that appears in 8, 24 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 24 and 40 two numbers at a time?

Yes. The LCM of 8 and 24 is 24, and the LCM of 24 and 40 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 8, 24 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 24 and 120 ÷ 40 all come out whole. Any other common multiple of 8, 24 and 40 is a multiple of 120.

See Also