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    LCM for 18, 27 and 45

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

    What's the Least Common Multiple (LCM) of 18, 27 and 45?

    Answer

    LCM of 18, 27 and 45 is
    270

    (Two hundred seventy)

    270 is the smallest positive integer that 18, 27 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 27 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

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

    Prime factor182745Highest power
    22——2
    332333233
    5——55

    LCM = 2 × 33 × 5 = 270

    Checking the LCM of 18, 27 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(18, 27) = (18 × 27) ÷ 9 = 486 ÷ 9 = 54

    LCM(54, 45) = (54 × 45) ÷ 9 = 2,430 ÷ 9 = 270

    LCM(18, 27, 45) = 270

    The pairs may be taken in any order — 27 and 45 first, then 18 — and the answer is the same 270. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 18, 27 and 45?. The LCM of 18, 27 and 45 is 270 — 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
    182730270
    1827311,674
    182732864
    182733594
    182734918
    1827351,890
    182736108
    1827371,998
    1827381,026
    182739702
    1827401,080
    1827412,214
    182742378
    1827432,322
    1827441,188
    182745270
    1827461,242
    1827472,538
    182748432
    1827492,646
    1827501,350
    182751918
    1827521,404
    1827532,862
    18275454
    1827552,970
    1827561,512
    1827571,026
    1827581,566
    1827593,186

    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 18, 27 and 45? (The answer is: 270). Enter the first number (e.g. '18'), the second (e.g. '27') 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 18, 27 and 45?

    LCM of 18, 27 and 45 is 270

    How to find the LCM of 18, 27 and 45 by prime factorization?

    Take every prime that appears in 18, 27 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3³ × 5 = 270.

    Can you get the LCM of 18, 27 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 27 is 54, and the LCM of 54 and 45 is 270 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 270 divisible by 18, 27 and 45?

    Yes, and by definition it is the smallest positive integer that is: 270 ÷ 18, 270 ÷ 27 and 270 ÷ 45 all come out whole. Any other common multiple of 18, 27 and 45 is a multiple of 270.

    See Also