LCM for 3, 9 and 15

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 3, 9 and 15?

Answer

LCM of 3, 9 and 15 is
45

First common multiples: 45, 90, 135, …

45 is divisible by all three: 45 ÷ 3 = 15, 45 ÷ 9 = 5, 45 ÷ 15 = 3 — and 15, 5 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 15 and of y/9 by 5 and of z/15 by 3.

3 — prime

9 = 32

15 = 3 × 5

Prime3915Highest power
3332332
5——55

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

LCM = 32 × 5 = 45

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LCM Table

1st2nd3rdLCM
1399
23918
3399
34936
35945
36918
37963
38972
3999
391090
391199
391236
3913117
3914126
391545
3916144
3917153
391818
3919171
3920180
392163
3922198
3923207
392472
3925225
3926234
392727
3928252
3929261
393090

FAQ

What's the Least Common Multiple (LCM) of 3, 9 and 15?

LCM of 3, 9 and 15 is 45

How to find the LCM of 3, 9 and 15 by prime factorization?

Take every prime that appears in 3, 9 and 15 to the highest power it reaches in any one of them and multiply: 3² × 5 = 45.

Can you get the LCM of 3, 9 and 15 two numbers at a time?

Yes. The LCM of 3 and 9 is 9, and the LCM of 9 and 15 is 45 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 45 divisible by 3, 9 and 15?

Yes, and by definition it is the smallest positive integer that is: 45 ÷ 3, 45 ÷ 9 and 45 ÷ 15 all come out whole. Any other common multiple of 3, 9 and 15 is a multiple of 45.

See Also