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    LCM for 12, 18 and 81

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

    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.

    Related Calculations

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    What is the LCM of 12, 18 and 81?. The LCM of 12, 18 and 81 is 324 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    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

    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

    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