LCM for 6, 12 and 30

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 6, 12 and 30?

Answer

LCM of 6, 12 and 30 is

First common multiples: 60, 120, 180, …

60 is divisible by all three: 60 ÷ 6 = 10, 60 ÷ 12 = 5, 60 ÷ 30 = 2 — and 10, 5 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/6 by 10 and of y/12 by 5 and of z/30 by 2.

6 = 2 × 3

12 = 2² × 3

30 = 2 × 3 × 5

Prime	6	12	30	Highest power
2	2	2²	2	2²
3	3	3	3	3
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 = 2² × 3 × 5 = 60

More with these numbers

Related Calculations

LCM Table

1st	2nd	3rd	LCM
6	12	15	60
6	12	16	48
6	12	17	204
6	12	18	36
6	12	19	228
6	12	20	60
6	12	21	84
6	12	22	132
6	12	23	276
6	12	24	24
6	12	25	300
6	12	26	156
6	12	27	108
6	12	28	84
6	12	29	348
6	12	30	60
6	12	31	372
6	12	32	96
6	12	33	132
6	12	34	204
6	12	35	420
6	12	36	36
6	12	37	444
6	12	38	228
6	12	39	156
6	12	40	120
6	12	41	492
6	12	42	84
6	12	43	516
6	12	44	132

FAQ

What's the Least Common Multiple (LCM) of 6, 12 and 30?

LCM of 6, 12 and 30 is 60

How to find the LCM of 6, 12 and 30 by prime factorization?

Take every prime that appears in 6, 12 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

Can you get the LCM of 6, 12 and 30 two numbers at a time?

Yes. The LCM of 6 and 12 is 12, and the LCM of 12 and 30 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 60 divisible by 6, 12 and 30?

Yes, and by definition it is the smallest positive integer that is: 60 ÷ 6, 60 ÷ 12 and 60 ÷ 30 all come out whole. Any other common multiple of 6, 12 and 30 is a multiple of 60.

LCM for 6, 12 and 30

What's the Least Common Multiple (LCM) of 6, 12 and 30?

More with these numbers

Related Calculations

See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 6, 12 and 30?

How to find the LCM of 6, 12 and 30 by prime factorization?

Can you get the LCM of 6, 12 and 30 two numbers at a time?

Is 60 divisible by 6, 12 and 30?

See Also

1st	2nd	3rd	LCM
6	12	15	60
6	12	16	48
6	12	17	204
6	12	18	36
6	12	19	228
6	12	20	60
6	12	21	84
6	12	22	132
6	12	23	276
6	12	24	24
6	12	25	300
6	12	26	156
6	12	27	108
6	12	28	84
6	12	29	348
6	12	30	60
6	12	31	372
6	12	32	96
6	12	33	132
6	12	34	204
6	12	35	420
6	12	36	36
6	12	37	444
6	12	38	228
6	12	39	156
6	12	40	120
6	12	41	492
6	12	42	84
6	12	43	516
6	12	44	132

1st	2nd	3rd	LCM
6	12	15	60
6	12	16	48
6	12	17	204
6	12	18	36
6	12	19	228
6	12	20	60
6	12	21	84
6	12	22	132
6	12	23	276
6	12	24	24
6	12	25	300
6	12	26	156
6	12	27	108
6	12	28	84
6	12	29	348
6	12	30	60
6	12	31	372
6	12	32	96
6	12	33	132
6	12	34	204
6	12	35	420
6	12	36	36
6	12	37	444
6	12	38	228
6	12	39	156
6	12	40	120
6	12	41	492
6	12	42	84
6	12	43	516
6	12	44	132

1st	2nd	3rd	LCM
6	12	15	60
6	12	16	48
6	12	17	204
6	12	18	36
6	12	19	228
6	12	20	60
6	12	21	84
6	12	22	132
6	12	23	276
6	12	24	24
6	12	25	300
6	12	26	156
6	12	27	108
6	12	28	84
6	12	29	348
6	12	30	60
6	12	31	372
6	12	32	96
6	12	33	132
6	12	34	204
6	12	35	420
6	12	36	36
6	12	37	444
6	12	38	228
6	12	39	156
6	12	40	120
6	12	41	492
6	12	42	84
6	12	43	516
6	12	44	132