LCM for 2, 8 and 9

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 2, 8 and 9?

Answer

LCM of 2, 8 and 9 is

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 2 = 36, 72 ÷ 8 = 9, 72 ÷ 9 = 8 — and 36, 9 and 8 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 36 and of y/8 by 9 and of z/9 by 8.

2 — prime

8 = 2³

9 = 3²

Prime	2	8	9	Highest power
2	2	2³	—	2³
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 = 2³ × 3² = 72

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LCM Table

1st	2nd	3rd	LCM
1	2	8	8
2	2	8	8
2	3	8	24
2	4	8	8
2	5	8	40
2	6	8	24
2	7	8	56
2	8	8	8
2	8	9	72
2	8	10	40
2	8	11	88
2	8	12	24
2	8	13	104
2	8	14	56
2	8	15	120
2	8	16	16
2	8	17	136
2	8	18	72
2	8	19	152
2	8	20	40
2	8	21	168
2	8	22	88
2	8	23	184
2	8	24	24
2	8	25	200
2	8	26	104
2	8	27	216
2	8	28	56
2	8	29	232
2	8	30	120

FAQ

What's the Least Common Multiple (LCM) of 2, 8 and 9?

LCM of 2, 8 and 9 is 72

How to find the LCM of 2, 8 and 9 by prime factorization?

Take every prime that appears in 2, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 2, 8 and 9 two numbers at a time?

Yes. The LCM of 2 and 8 is 8, and the LCM of 8 and 9 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 2, 8 and 9?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 2, 72 ÷ 8 and 72 ÷ 9 all come out whole. Any other common multiple of 2, 8 and 9 is a multiple of 72.

LCM for 2, 8 and 9

What's the Least Common Multiple (LCM) of 2, 8 and 9?

More with these numbers

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See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 2, 8 and 9?

How to find the LCM of 2, 8 and 9 by prime factorization?

Can you get the LCM of 2, 8 and 9 two numbers at a time?

Is 72 divisible by 2, 8 and 9?

See Also

1st	2nd	3rd	LCM
1	2	8	8
2	2	8	8
2	3	8	24
2	4	8	8
2	5	8	40
2	6	8	24
2	7	8	56
2	8	8	8
2	8	9	72
2	8	10	40
2	8	11	88
2	8	12	24
2	8	13	104
2	8	14	56
2	8	15	120
2	8	16	16
2	8	17	136
2	8	18	72
2	8	19	152
2	8	20	40
2	8	21	168
2	8	22	88
2	8	23	184
2	8	24	24
2	8	25	200
2	8	26	104
2	8	27	216
2	8	28	56
2	8	29	232
2	8	30	120

1st	2nd	3rd	LCM
1	2	8	8
2	2	8	8
2	3	8	24
2	4	8	8
2	5	8	40
2	6	8	24
2	7	8	56
2	8	8	8
2	8	9	72
2	8	10	40
2	8	11	88
2	8	12	24
2	8	13	104
2	8	14	56
2	8	15	120
2	8	16	16
2	8	17	136
2	8	18	72
2	8	19	152
2	8	20	40
2	8	21	168
2	8	22	88
2	8	23	184
2	8	24	24
2	8	25	200
2	8	26	104
2	8	27	216
2	8	28	56
2	8	29	232
2	8	30	120

1st	2nd	3rd	LCM
1	2	8	8
2	2	8	8
2	3	8	24
2	4	8	8
2	5	8	40
2	6	8	24
2	7	8	56
2	8	8	8
2	8	9	72
2	8	10	40
2	8	11	88
2	8	12	24
2	8	13	104
2	8	14	56
2	8	15	120
2	8	16	16
2	8	17	136
2	8	18	72
2	8	19	152
2	8	20	40
2	8	21	168
2	8	22	88
2	8	23	184
2	8	24	24
2	8	25	200
2	8	26	104
2	8	27	216
2	8	28	56
2	8	29	232
2	8	30	120