LCM for 2, 3 and 9

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 2, 3 and 9?

Answer

LCM of 2, 3 and 9 is

First common multiples: 18, 36, 54, …

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

2 — prime

3 — prime

9 = 3²

Prime	2	3	9	Highest power
2	2	—	—	2
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

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Related Calculations

LCM Table

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

FAQ

What's the Least Common Multiple (LCM) of 2, 3 and 9?

LCM of 2, 3 and 9 is 18

How to find the LCM of 2, 3 and 9 by prime factorization?

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

Can you get the LCM of 2, 3 and 9 two numbers at a time?

Yes. The LCM of 2 and 3 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 2, 3 and 9?

Yes, and by definition it is the smallest positive integer that is: 18 ÷ 2, 18 ÷ 3 and 18 ÷ 9 all come out whole. Any other common multiple of 2, 3 and 9 is a multiple of 18.

LCM for 2, 3 and 9

What's the Least Common Multiple (LCM) of 2, 3 and 9?

More with these numbers

Related Calculations

See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 2, 3 and 9?

How to find the LCM of 2, 3 and 9 by prime factorization?

Can you get the LCM of 2, 3 and 9 two numbers at a time?

Is 18 divisible by 2, 3 and 9?

See Also

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

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

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