LCM for 6, 9 and 24

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What's the Least Common Multiple (LCM) of 6, 9 and 24?

Answer

LCM of 6, 9 and 24 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 6 = 12, 72 ÷ 9 = 8, 72 ÷ 24 = 3 — and 12, 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/6 by 12 and of y/9 by 8 and of z/24 by 3.

6 = 2 × 3

9 = 32

24 = 23 × 3

Prime6924Highest power
22—2323
3332332

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

LCM = 23 × 32 = 72

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LCM Table

1st2nd3rdLCM
69918
691090
6911198
691236
6913234
6914126
691590
6916144
6917306
691818
6919342
6920180
6921126
6922198
6923414
692472
6925450
6926234
692754
6928252
6929522
693090
6931558
6932288
6933198
6934306
6935630
693636
6937666
6938342

FAQ

What's the Least Common Multiple (LCM) of 6, 9 and 24?

LCM of 6, 9 and 24 is 72

How to find the LCM of 6, 9 and 24 by prime factorization?

Take every prime that appears in 6, 9 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 6, 9 and 24 two numbers at a time?

Yes. The LCM of 6 and 9 is 18, and the LCM of 18 and 24 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 6, 9 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 6, 72 ÷ 9 and 72 ÷ 24 all come out whole. Any other common multiple of 6, 9 and 24 is a multiple of 72.

See Also