LCM for 8, 16 and 24

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What's the Least Common Multiple (LCM) of 8, 16 and 24?

Answer

LCM of 8, 16 and 24 is
48

First common multiples: 48, 96, 144, …

48 is divisible by all three: 48 ÷ 8 = 6, 48 ÷ 16 = 3, 48 ÷ 24 = 2 — and 6, 3 and 2 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 6 and of y/16 by 3 and of z/24 by 2.

8 = 23

16 = 24

24 = 23 × 3

Prime81624Highest power
223242324
3——33

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

LCM = 24 × 3 = 48

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LCM Table

1st2nd3rdLCM
8916144
8101680
81116176
8121648
81316208
81416112
81516240
8161616
81617272
81618144
81619304
8162080
81621336
81622176
81623368
8162448
81625400
81626208
81627432
81628112
81629464
81630240
81631496
8163232
81633528
81634272
81635560
81636144
81637592
81638304

FAQ

What's the Least Common Multiple (LCM) of 8, 16 and 24?

LCM of 8, 16 and 24 is 48

How to find the LCM of 8, 16 and 24 by prime factorization?

Take every prime that appears in 8, 16 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

Can you get the LCM of 8, 16 and 24 two numbers at a time?

Yes. The LCM of 8 and 16 is 16, and the LCM of 16 and 24 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 48 divisible by 8, 16 and 24?

Yes, and by definition it is the smallest positive integer that is: 48 ÷ 8, 48 ÷ 16 and 48 ÷ 24 all come out whole. Any other common multiple of 8, 16 and 24 is a multiple of 48.

See Also