LCM for 10, 12 and 40

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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

Prime101240Highest power
22222323
3—3—3
55—55

— = 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

1st2nd3rdLCM
101225300
101226780
101227540
101228420
1012291,740
10123060
1012311,860
101232480
101233660
1012341,020
101235420
101236180
1012372,220
1012381,140
101239780
101240120
1012412,460
101242420
1012432,580
101244660
101245180
1012461,380
1012472,820
101248240
1012492,940
101250300
1012511,020
101252780
1012533,180
101254540

FAQ

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

LCM of 10, 12 and 40 is 120

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

Take every prime that appears in 10, 12 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

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

Yes. The LCM of 10 and 12 is 60, and the LCM of 60 and 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 10, 12 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 12 and 120 ÷ 40 all come out whole. Any other common multiple of 10, 12 and 40 is a multiple of 120.

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