LCM for 3, 6 and 9

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 3, 6 and 9?

Answer

LCM of 3, 6 and 9 is

First common multiples: 18, 36, 54, …

18 is divisible by all three: 18 ÷ 3 = 6, 18 ÷ 6 = 3, 18 ÷ 9 = 2 — and 6, 3 and 2 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 6 and of y/6 by 3 and of z/9 by 2.

3 — prime

6 = 2 × 3

9 = 3²

Prime	3	6	9	Highest power
2	—	2	—	2
3	3	3	3²	3²

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

LCM = 2 × 3² = 18

More with these numbers

Related Calculations

LCM Table

1st	2nd	3rd	LCM
1	3	6	6
2	3	6	6
3	3	6	6
3	4	6	12
3	5	6	30
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30

FAQ

What's the Least Common Multiple (LCM) of 3, 6 and 9?

LCM of 3, 6 and 9 is 18

How to find the LCM of 3, 6 and 9 by prime factorization?

Take every prime that appears in 3, 6 and 9 to the highest power it reaches in any one of them and multiply: 2 × 3² = 18.

Can you get the LCM of 3, 6 and 9 two numbers at a time?

Yes. The LCM of 3 and 6 is 6, and the LCM of 6 and 9 is 18 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 18 divisible by 3, 6 and 9?

Yes, and by definition it is the smallest positive integer that is: 18 ÷ 3, 18 ÷ 6 and 18 ÷ 9 all come out whole. Any other common multiple of 3, 6 and 9 is a multiple of 18.

LCM for 3, 6 and 9

What's the Least Common Multiple (LCM) of 3, 6 and 9?

More with these numbers

Related Calculations

See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 3, 6 and 9?

How to find the LCM of 3, 6 and 9 by prime factorization?

Can you get the LCM of 3, 6 and 9 two numbers at a time?

Is 18 divisible by 3, 6 and 9?

See Also

1st	2nd	3rd	LCM
1	3	6	6
2	3	6	6
3	3	6	6
3	4	6	12
3	5	6	30
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30

1st	2nd	3rd	LCM
1	3	6	6
2	3	6	6
3	3	6	6
3	4	6	12
3	5	6	30
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30

1st	2nd	3rd	LCM
1	3	6	6
2	3	6	6
3	3	6	6
3	4	6	12
3	5	6	30
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30