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    LCM for 15, 23 and 27

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

    What's the Least Common Multiple (LCM) of 15, 23 and 27?

    Answer

    LCM of 15, 23 and 27 is
    3,105

    (Three thousand one hundred five)

    3,105 is the smallest positive integer that 15, 23 and 27 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 23 and 27 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 23: 23 (exponent form: 23)

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

    Prime factor152327Highest power
    33—3333
    55——5
    23—23—23

    LCM = 33 × 5 × 23 = 3,105

    Checking the LCM of 15, 23 and 27 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, 23) = (15 × 23) ÷ 1 = 345 ÷ 1 = 345

    LCM(345, 27) = (345 × 27) ÷ 3 = 9,315 ÷ 3 = 3,105

    LCM(15, 23, 27) = 3,105

    The pairs may be taken in any order — 23 and 27 first, then 15 — and the answer is the same 3,105. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 23 and 27?. The LCM of 15, 23 and 27 is 3,105 — 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
    1215231,380
    1315234,485
    1415234,830
    151523345
    1516235,520
    1517235,865
    1518232,070
    1519236,555
    1520231,380
    1521232,415
    1522237,590
    152323345
    1523242,760
    1523251,725
    1523268,970
    1523273,105
    1523289,660
    15232910,005
    152330690
    15233110,695
    15233211,040
    1523333,795
    15233411,730
    1523352,415
    1523364,140
    15233712,765
    15233813,110
    1523394,485
    1523402,760
    15234114,145

    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, 23 and 27? (The answer is: 3,105). Enter the first number (e.g. '15'), the second (e.g. '23') and the third (e.g. '27'), 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, 23 and 27?

    LCM of 15, 23 and 27 is 3,105

    How to find the LCM of 15, 23 and 27 by prime factorization?

    Take every prime that appears in 15, 23 and 27 to the highest power it reaches in any one of them and multiply: 3³ × 5 × 23 = 3,105.

    Can you get the LCM of 15, 23 and 27 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 23 is 345, and the LCM of 345 and 27 is 3,105 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 3,105 divisible by 15, 23 and 27?

    Yes, and by definition it is the smallest positive integer that is: 3,105 ÷ 15, 3,105 ÷ 23 and 3,105 ÷ 27 all come out whole. Any other common multiple of 15, 23 and 27 is a multiple of 3,105.

    See Also