What is the LCM of 10, 12 and 40?

What's the Least Common Multiple (LCM) of 10, 12 and 40?

Answer

LCM of 10, 12 and 40 is

120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 10 = 12, 120 ÷ 12 = 10, 120 ÷ 40 = 3 — and 12, 10 and 3 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/10 by 12 and of y/12 by 10 and of z/40 by 3.

10 = 2 × 5

12 = 2² × 3

40 = 2³ × 5

Prime	10	12	40	Highest power
2	2	2²	2³	2³
3	—	3	—	3
5	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 = 2³ × 3 × 5 = 120

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LCM Table

1st	2nd	3rd	LCM
10	12	25	300
10	12	26	780
10	12	27	540
10	12	28	420
10	12	29	1,740
10	12	30	60
10	12	31	1,860
10	12	32	480
10	12	33	660
10	12	34	1,020
10	12	35	420
10	12	36	180
10	12	37	2,220
10	12	38	1,140
10	12	39	780
10	12	40	120
10	12	41	2,460
10	12	42	420
10	12	43	2,580
10	12	44	660
10	12	45	180
10	12	46	1,380
10	12	47	2,820
10	12	48	240
10	12	49	2,940
10	12	50	300
10	12	51	1,020
10	12	52	780
10	12	53	3,180
10	12	54	540

LCM for 10, 12 and 40

What's the Least Common Multiple (LCM) of 10, 12 and 40?

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Related Calculations

See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 10, 12 and 40?

How to find the LCM of 10, 12 and 40 by prime factorization?

Can you get the LCM of 10, 12 and 40 two numbers at a time?

Is 120 divisible by 10, 12 and 40?

See Also