LCM for 8, 24 and 64

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What's the Least Common Multiple (LCM) of 8, 24 and 64?

Answer

LCM of 8, 24 and 64 is
192

First common multiples: 192, 384, 576, …

192 is divisible by all three: 192 ÷ 8 = 24, 192 ÷ 24 = 8, 192 ÷ 64 = 3 — and 24, 8 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 24 and of y/24 by 8 and of z/64 by 3.

8 = 23

24 = 23 × 3

64 = 26

Prime82464Highest power
223232626
3—3—3

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

LCM = 26 × 3 = 192

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LCM Table

1st2nd3rdLCM
824491,176
82450600
82451408
82452312
824531,272
82454216
824551,320
82456168
82457456
82458696
824591,416
82460120
824611,464
82462744
82463504
82464192
824651,560
82466264
824671,608
82468408
82469552
82470840
824711,704
8247272
824731,752
82474888
82475600
82476456
824771,848
82478312

FAQ

What's the Least Common Multiple (LCM) of 8, 24 and 64?

LCM of 8, 24 and 64 is 192

How to find the LCM of 8, 24 and 64 by prime factorization?

Take every prime that appears in 8, 24 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

Can you get the LCM of 8, 24 and 64 two numbers at a time?

Yes. The LCM of 8 and 24 is 24, and the LCM of 24 and 64 is 192 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 192 divisible by 8, 24 and 64?

Yes, and by definition it is the smallest positive integer that is: 192 ÷ 8, 192 ÷ 24 and 192 ÷ 64 all come out whole. Any other common multiple of 8, 24 and 64 is a multiple of 192.

See Also