LCM for 3, 9 and 12

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 3, 9 and 12?

Answer

LCM of 3, 9 and 12 is
36

First common multiples: 36, 72, 108, …

36 is divisible by all three: 36 ÷ 3 = 12, 36 ÷ 9 = 4, 36 ÷ 12 = 3 — and 12, 4 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 12 and of y/9 by 4 and of z/12 by 3.

3 — prime

9 = 32

12 = 22 × 3

Prime3912Highest power
2——2222
3332332

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

LCM = 22 × 32 = 36

More with these numbers

Related Calculations

See Also

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 12?

LCM of 3, 9 and 12 is 36

How to find the LCM of 3, 9 and 12 by prime factorization?

Take every prime that appears in 3, 9 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

Can you get the LCM of 3, 9 and 12 two numbers at a time?

Yes. The LCM of 3 and 9 is 9, and the LCM of 9 and 12 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 36 divisible by 3, 9 and 12?

Yes, and by definition it is the smallest positive integer that is: 36 ÷ 3, 36 ÷ 9 and 36 ÷ 12 all come out whole. Any other common multiple of 3, 9 and 12 is a multiple of 36.

See Also