LCM for 12, 22 and 40

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What's the Least Common Multiple (LCM) of 12, 22 and 40?

Answer

LCM of 12, 22 and 40 is
1,320

First common multiples: 1,320; 2,640; 3,960; …

1,320 is divisible by all three: 1,320 ÷ 12 = 110; 1,320 ÷ 22 = 60; 1,320 ÷ 40 = 33 — and 110, 60 and 33 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 110 and of y/22 by 60 and of z/40 by 33.

12 = 22 × 3

22 = 2 × 11

40 = 23 × 5

Prime122240Highest power
22222323
33——3
5——55
11—11—11

— = 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 × 11 = 1,320

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LCM Table

1st2nd3rdLCM
1222253,300
1222261,716
1222271,188
122228924
1222293,828
122230660
1222314,092
1222321,056
122233132
1222342,244
1222354,620
122236396
1222374,884
1222382,508
1222391,716
1222401,320
1222415,412
122242924
1222435,676
122244132
1222451,980
1222463,036
1222476,204
122248528
1222496,468
1222503,300
1222512,244
1222521,716
1222536,996
1222541,188

FAQ

What's the Least Common Multiple (LCM) of 12, 22 and 40?

LCM of 12, 22 and 40 is 1,320

How to find the LCM of 12, 22 and 40 by prime factorization?

Take every prime that appears in 12, 22 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 11 = 1,320.

Can you get the LCM of 12, 22 and 40 two numbers at a time?

Yes. The LCM of 12 and 22 is 132, and the LCM of 132 and 40 is 1,320 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,320 divisible by 12, 22 and 40?

Yes, and by definition it is the smallest positive integer that is: 1,320 ÷ 12, 1,320 ÷ 22 and 1,320 ÷ 40 all come out whole. Any other common multiple of 12, 22 and 40 is a multiple of 1,320.

See Also