LCM for 12, 18 and 81

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What's the Least Common Multiple (LCM) of 12, 18 and 81?

Answer

LCM of 12, 18 and 81 is
324

First common multiples: 324, 648, 972, …

324 is divisible by all three: 324 ÷ 12 = 27, 324 ÷ 18 = 18, 324 ÷ 81 = 4 — and 27, 18 and 4 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 27 and of y/18 by 18 and of z/81 by 4.

12 = 22 × 3

18 = 2 × 32

81 = 34

Prime121881Highest power
2222—22
33323434

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

LCM = 22 × 34 = 324

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LCM Table

1st2nd3rdLCM
121866396
1218672,412
121868612
121869828
1218701,260
1218712,556
12187272
1218732,628
1218741,332
121875900
121876684
1218772,772
121878468
1218792,844
121880720
121881324
1218821,476
1218832,988
121884252
1218853,060
1218861,548
1218871,044
121888792
1218893,204
121890180
1218913,276
121892828
1218931,116
1218941,692
1218953,420

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 81?

LCM of 12, 18 and 81 is 324

How to find the LCM of 12, 18 and 81 by prime factorization?

Take every prime that appears in 12, 18 and 81 to the highest power it reaches in any one of them and multiply: 2² × 3⁴ = 324.

Can you get the LCM of 12, 18 and 81 two numbers at a time?

Yes. The LCM of 12 and 18 is 36, and the LCM of 36 and 81 is 324 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 324 divisible by 12, 18 and 81?

Yes, and by definition it is the smallest positive integer that is: 324 ÷ 12, 324 ÷ 18 and 324 ÷ 81 all come out whole. Any other common multiple of 12, 18 and 81 is a multiple of 324.

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