LCM for 4, 21 and 24

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 4, 21 and 24?

Answer

LCM of 4, 21 and 24 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 4 = 42, 168 ÷ 21 = 8, 168 ÷ 24 = 7 — and 42, 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/4 by 42 and of y/21 by 8 and of z/24 by 7.

4 = 22

21 = 3 × 7

24 = 23 × 3

Prime42124Highest power
222—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
4921252
41021420
41121924
4122184
413211,092
4142184
41521420
41621336
417211,428
41821252
419211,596
42021420
4212184
42122924
421231,932
42124168
421252,100
421261,092
42127756
4212884
421292,436
42130420
421312,604
42132672
42133924
421341,428
42135420
42136252
421373,108
421381,596

FAQ

What's the Least Common Multiple (LCM) of 4, 21 and 24?

LCM of 4, 21 and 24 is 168

How to find the LCM of 4, 21 and 24 by prime factorization?

Take every prime that appears in 4, 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 4, 21 and 24 two numbers at a time?

Yes. The LCM of 4 and 21 is 84, and the LCM of 84 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 4, 21 and 24?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 4, 168 ÷ 21 and 168 ÷ 24 all come out whole. Any other common multiple of 4, 21 and 24 is a multiple of 168.

See Also