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    LCM for 27, 36 and 45

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

    What's the Least Common Multiple (LCM) of 27, 36 and 45?

    Answer

    LCM of 27, 36 and 45 is
    540

    (Five hundred forty)

    540 is the smallest positive integer that 27, 36 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 27, 36 and 45 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 27: 3 × 3 × 3 (exponent form: 33)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor273645Highest power
    2—22—22
    333323233
    5——55

    LCM = 22 × 33 × 5 = 540

    Checking the LCM of 27, 36 and 45 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(27, 36) = (27 × 36) ÷ 9 = 972 ÷ 9 = 108

    LCM(108, 45) = (108 × 45) ÷ 9 = 4,860 ÷ 9 = 540

    LCM(27, 36, 45) = 540

    The pairs may be taken in any order — 36 and 45 first, then 27 — and the answer is the same 540. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 27, 36 and 45?. The LCM of 27, 36 and 45 is 540 — 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
    273036540
    2731363,348
    273236864
    2733361,188
    2734361,836
    2735363,780
    273636108
    2736373,996
    2736382,052
    2736391,404
    2736401,080
    2736414,428
    273642756
    2736434,644
    2736441,188
    273645540
    2736462,484
    2736475,076
    273648432
    2736495,292
    2736502,700
    2736511,836
    2736521,404
    2736535,724
    273654108
    2736555,940
    2736561,512
    2736572,052
    2736583,132
    2736596,372

    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 27, 36 and 45? (The answer is: 540). Enter the first number (e.g. '27'), the second (e.g. '36') and the third (e.g. '45'), 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 27, 36 and 45?

    LCM of 27, 36 and 45 is 540

    How to find the LCM of 27, 36 and 45 by prime factorization?

    Take every prime that appears in 27, 36 and 45 to the highest power it reaches in any one of them and multiply: 2² × 3³ × 5 = 540.

    Can you get the LCM of 27, 36 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 27 and 36 is 108, and the LCM of 108 and 45 is 540 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 540 divisible by 27, 36 and 45?

    Yes, and by definition it is the smallest positive integer that is: 540 ÷ 27, 540 ÷ 36 and 540 ÷ 45 all come out whole. Any other common multiple of 27, 36 and 45 is a multiple of 540.

    See Also