LCM for 8, 21 and 24

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What's the Least Common Multiple (LCM) of 8, 21 and 24?

Answer

LCM of 8, 21 and 24 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 8 = 21, 168 ÷ 21 = 8, 168 ÷ 24 = 7 — and 21, 8 and 7 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 21 and of y/21 by 8 and of z/24 by 7.

8 = 23

21 = 3 × 7

24 = 23 × 3

Prime82124Highest power
223—2323
3—333
7—7—7

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

LCM = 23 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
8921504
81021840
811211,848
81221168
813212,184
81421168
81521840
81621336
817212,856
81821504
819213,192
82021840
82121168
821221,848
821233,864
82124168
821254,200
821262,184
821271,512
82128168
821294,872
82130840
821315,208
82132672
821331,848
821342,856
82135840
82136504
821376,216
821383,192

FAQ

What's the Least Common Multiple (LCM) of 8, 21 and 24?

LCM of 8, 21 and 24 is 168

How to find the LCM of 8, 21 and 24 by prime factorization?

Take every prime that appears in 8, 21 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 21 and 24 two numbers at a time?

Yes. The LCM of 8 and 21 is 168, and the LCM of 168 and 24 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 8, 21 and 24?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 21 and 168 ÷ 24 all come out whole. Any other common multiple of 8, 21 and 24 is a multiple of 168.

See Also