LCM for 12, 18 and 40

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What's the Least Common Multiple (LCM) of 12, 18 and 40?

Answer

LCM of 12, 18 and 40 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 12 = 30, 360 ÷ 18 = 20, 360 ÷ 40 = 9 — and 30, 20 and 9 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/12 by 30 and of y/18 by 20 and of z/40 by 9.

12 = 22 × 3

18 = 2 × 32

40 = 23 × 5

Prime121840Highest power
22222323
3332—32
5——55

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

LCM = 23 × 32 × 5 = 360

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LCM Table

1st2nd3rdLCM
121825900
121826468
121827108
121828252
1218291,044
121830180
1218311,116
121832288
121833396
121834612
1218351,260
12183636
1218371,332
121838684
121839468
121840360
1218411,476
121842252
1218431,548
121844396
121845180
121846828
1218471,692
121848144
1218491,764
121850900
121851612
121852468
1218531,908
121854108

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 40?

LCM of 12, 18 and 40 is 360

How to find the LCM of 12, 18 and 40 by prime factorization?

Take every prime that appears in 12, 18 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 12, 18 and 40 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 40 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 12, 18 and 40?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 12, 360 ÷ 18 and 360 ÷ 40 all come out whole. Any other common multiple of 12, 18 and 40 is a multiple of 360.

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