LCM for 6, 15 and 18

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 6, 15 and 18?

Answer

LCM of 6, 15 and 18 is

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 6 = 15, 90 ÷ 15 = 6, 90 ÷ 18 = 5 — and 15, 6 and 5 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/6 by 15 and of y/15 by 6 and of z/18 by 5.

6 = 2 × 3

15 = 3 × 5

18 = 2 × 3²

Prime	6	15	18	Highest power
2	2	—	2	2
3	3	3	3²	3²
5	—	5	—	5

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

LCM = 2 × 3² × 5 = 90

More with these numbers

Related Calculations

LCM Table

1st	2nd	3rd	LCM
3	6	15	30
4	6	15	60
5	6	15	30
6	6	15	30
6	7	15	210
6	8	15	120
6	9	15	90
6	10	15	30
6	11	15	330
6	12	15	60
6	13	15	390
6	14	15	210
6	15	15	30
6	15	16	240
6	15	17	510
6	15	18	90
6	15	19	570
6	15	20	60
6	15	21	210
6	15	22	330
6	15	23	690
6	15	24	120
6	15	25	150
6	15	26	390
6	15	27	270
6	15	28	420
6	15	29	870
6	15	30	30
6	15	31	930
6	15	32	480

FAQ

What's the Least Common Multiple (LCM) of 6, 15 and 18?

LCM of 6, 15 and 18 is 90

How to find the LCM of 6, 15 and 18 by prime factorization?

Take every prime that appears in 6, 15 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 6, 15 and 18 two numbers at a time?

Yes. The LCM of 6 and 15 is 30, and the LCM of 30 and 18 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 6, 15 and 18?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 6, 90 ÷ 15 and 90 ÷ 18 all come out whole. Any other common multiple of 6, 15 and 18 is a multiple of 90.

LCM for 6, 15 and 18

What's the Least Common Multiple (LCM) of 6, 15 and 18?

More with these numbers

Related Calculations

See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 6, 15 and 18?

How to find the LCM of 6, 15 and 18 by prime factorization?

Can you get the LCM of 6, 15 and 18 two numbers at a time?

Is 90 divisible by 6, 15 and 18?

See Also

1st	2nd	3rd	LCM
3	6	15	30
4	6	15	60
5	6	15	30
6	6	15	30
6	7	15	210
6	8	15	120
6	9	15	90
6	10	15	30
6	11	15	330
6	12	15	60
6	13	15	390
6	14	15	210
6	15	15	30
6	15	16	240
6	15	17	510
6	15	18	90
6	15	19	570
6	15	20	60
6	15	21	210
6	15	22	330
6	15	23	690
6	15	24	120
6	15	25	150
6	15	26	390
6	15	27	270
6	15	28	420
6	15	29	870
6	15	30	30
6	15	31	930
6	15	32	480

1st	2nd	3rd	LCM
3	6	15	30
4	6	15	60
5	6	15	30
6	6	15	30
6	7	15	210
6	8	15	120
6	9	15	90
6	10	15	30
6	11	15	330
6	12	15	60
6	13	15	390
6	14	15	210
6	15	15	30
6	15	16	240
6	15	17	510
6	15	18	90
6	15	19	570
6	15	20	60
6	15	21	210
6	15	22	330
6	15	23	690
6	15	24	120
6	15	25	150
6	15	26	390
6	15	27	270
6	15	28	420
6	15	29	870
6	15	30	30
6	15	31	930
6	15	32	480

1st	2nd	3rd	LCM
3	6	15	30
4	6	15	60
5	6	15	30
6	6	15	30
6	7	15	210
6	8	15	120
6	9	15	90
6	10	15	30
6	11	15	330
6	12	15	60
6	13	15	390
6	14	15	210
6	15	15	30
6	15	16	240
6	15	17	510
6	15	18	90
6	15	19	570
6	15	20	60
6	15	21	210
6	15	22	330
6	15	23	690
6	15	24	120
6	15	25	150
6	15	26	390
6	15	27	270
6	15	28	420
6	15	29	870
6	15	30	30
6	15	31	930
6	15	32	480