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    LCM for 15, 27 and 45

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

    What's the Least Common Multiple (LCM) of 15, 27 and 45?

    Answer

    LCM of 15, 27 and 45 is
    135

    (One hundred thirty-five)

    135 is the smallest positive integer that 15, 27 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 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 15: 3 × 5 (exponent form: 3 × 5)

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

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

    Prime factor152745Highest power
    33333233
    55—55

    LCM = 33 × 5 = 135

    Checking the LCM of 15, 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(15, 27) = (15 × 27) ÷ 3 = 405 ÷ 3 = 135

    LCM(135, 45) = (135 × 45) ÷ 45 = 6,075 ÷ 45 = 135

    LCM(15, 27, 45) = 135

    The pairs may be taken in any order — 27 and 45 first, then 15 — and the answer is the same 135. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 27 and 45?. The LCM of 15, 27 and 45 is 135 — 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
    152730270
    1527314,185
    1527324,320
    1527331,485
    1527344,590
    152735945
    152736540
    1527374,995
    1527385,130
    1527391,755
    1527401,080
    1527415,535
    1527421,890
    1527435,805
    1527445,940
    152745135
    1527466,210
    1527476,345
    1527482,160
    1527496,615
    1527501,350
    1527512,295
    1527527,020
    1527537,155
    152754270
    1527551,485
    1527567,560
    1527572,565
    1527587,830
    1527597,965

    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 15, 27 and 45? (The answer is: 135). Enter the first number (e.g. '15'), 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 15, 27 and 45?

    LCM of 15, 27 and 45 is 135

    How to find the LCM of 15, 27 and 45 by prime factorization?

    Take every prime that appears in 15, 27 and 45 to the highest power it reaches in any one of them and multiply: 3³ × 5 = 135.

    Can you get the LCM of 15, 27 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 27 is 135, and the LCM of 135 and 45 is 135 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 135 divisible by 15, 27 and 45?

    Yes, and by definition it is the smallest positive integer that is: 135 ÷ 15, 135 ÷ 27 and 135 ÷ 45 all come out whole. Any other common multiple of 15, 27 and 45 is a multiple of 135.

    See Also