LCM for 10, 11 and 12

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What's the Least Common Multiple (LCM) of 10, 11 and 12?

Answer

LCM of 10, 11 and 12 is
660

First common multiples: 660; 1,320; 1,980; …

660 is divisible by all three: 660 ÷ 10 = 66, 660 ÷ 11 = 60, 660 ÷ 12 = 55 — and 66, 60 and 55 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 66 and of y/11 by 60 and of z/12 by 55.

10 = 2 × 5

11 — prime

12 = 22 × 3

Prime101112Highest power
22—2222
3——33
55——5
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 = 22 × 3 × 5 × 11 = 660

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LCM Table

1st2nd3rdLCM
11011110
21011110
31011330
41011220
51011110
61011330
71011770
81011440
91011990
101011110
101111110
101112660
1011131,430
101114770
101115330
101116880
1011171,870
101118990
1011192,090
101120220
1011212,310
101122110
1011232,530
1011241,320
101125550
1011261,430
1011272,970
1011281,540
1011293,190
101130330

FAQ

What's the Least Common Multiple (LCM) of 10, 11 and 12?

LCM of 10, 11 and 12 is 660

How to find the LCM of 10, 11 and 12 by prime factorization?

Take every prime that appears in 10, 11 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 11 = 660.

Can you get the LCM of 10, 11 and 12 two numbers at a time?

Yes. The LCM of 10 and 11 is 110, and the LCM of 110 and 12 is 660 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 660 divisible by 10, 11 and 12?

Yes, and by definition it is the smallest positive integer that is: 660 ÷ 10, 660 ÷ 11 and 660 ÷ 12 all come out whole. Any other common multiple of 10, 11 and 12 is a multiple of 660.

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