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    LCM for 4, 27 and 36

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

    What's the Least Common Multiple (LCM) of 4, 27 and 36?

    Answer

    LCM of 4, 27 and 36 is
    108

    (One hundred eight)

    108 is the smallest positive integer that 4, 27 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 27 and 36 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 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

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

    Prime factor42736Highest power
    222—2222
    3—333233

    LCM = 22 × 33 = 108

    Checking the LCM of 4, 27 and 36 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(4, 27) = (4 × 27) ÷ 1 = 108 ÷ 1 = 108

    LCM(108, 36) = (108 × 36) ÷ 36 = 3,888 ÷ 36 = 108

    LCM(4, 27, 36) = 108

    The pairs may be taken in any order — 27 and 36 first, then 4 — and the answer is the same 108. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 4, 27 and 36?. The LCM of 4, 27 and 36 is 108 — 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
    42127756
    422271,188
    423272,484
    42427216
    425272,700
    426271,404
    42727108
    42728756
    427293,132
    42730540
    427313,348
    42732864
    427331,188
    427341,836
    427353,780
    42736108
    427373,996
    427382,052
    427391,404
    427401,080
    427414,428
    42742756
    427434,644
    427441,188
    42745540
    427462,484
    427475,076
    42748432
    427495,292
    427502,700

    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 4, 27 and 36? (The answer is: 108). Enter the first number (e.g. '4'), the second (e.g. '27') and the third (e.g. '36'), 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 4, 27 and 36?

    LCM of 4, 27 and 36 is 108

    How to find the LCM of 4, 27 and 36 by prime factorization?

    Take every prime that appears in 4, 27 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3³ = 108.

    Can you get the LCM of 4, 27 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 27 is 108, and the LCM of 108 and 36 is 108 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 108 divisible by 4, 27 and 36?

    Yes, and by definition it is the smallest positive integer that is: 108 ÷ 4, 108 ÷ 27 and 108 ÷ 36 all come out whole. Any other common multiple of 4, 27 and 36 is a multiple of 108.

    See Also