LCM for 12, 18 and 81

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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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

(Three hundred twenty-four)

324 is the smallest positive integer that 12, 18 and 81 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 18 and 81 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 81: 3 × 3 × 3 × 3 (exponent form: 34)

Prime factor121881Highest power
2222—22
33323434

LCM = 22 × 34 = 324

Checking the LCM of 12, 18 and 81 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(12, 18) = (12 × 18) ÷ 6 = 216 ÷ 6 = 36

LCM(36, 81) = (36 × 81) ÷ 9 = 2,916 ÷ 9 = 324

LCM(12, 18, 81) = 324

The pairs may be taken in any order — 18 and 81 first, then 12 — and the answer is the same 324. That is exactly why the two routes on this page agree.

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 12, 18 and 81? (The answer is: 324). Enter the first number (e.g. '12'), the second (e.g. '18') and the third (e.g. '81'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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.

See Also