LCM for 3, 9 and 24

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 9 and 24?

Answer

LCM of 3, 9 and 24 is
72

First common multiples: 72, 144, 216, …

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

3 — prime

9 = 32

24 = 23 × 3

Prime3924Highest power
2——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
3999
391090
391199
391236
3913117
3914126
391545
3916144
3917153
391818
3919171
3920180
392163
3922198
3923207
392472
3925225
3926234
392727
3928252
3929261
393090
3931279
3932288
393399
3934306
3935315
393636
3937333
3938342

FAQ

What's the Least Common Multiple (LCM) of 3, 9 and 24?

LCM of 3, 9 and 24 is 72

How to find the LCM of 3, 9 and 24 by prime factorization?

Take every prime that appears in 3, 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 3, 9 and 24 two numbers at a time?

Yes. The LCM of 3 and 9 is 9, and the LCM of 9 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 3, 9 and 24?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 3, 72 ÷ 9 and 72 ÷ 24 all come out whole. Any other common multiple of 3, 9 and 24 is a multiple of 72.

See Also