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    LCM for 18, 24 and 60

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

    What's the Least Common Multiple (LCM) of 18, 24 and 60?

    Answer

    LCM of 18, 24 and 60 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 18, 24 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 24 and 60 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    Prime factor182460Highest power
    22232223
    3323332
    5——55

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 18, 24 and 60 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, 24) = (18 × 24) ÷ 6 = 432 ÷ 6 = 72

    LCM(72, 60) = (72 × 60) ÷ 12 = 4,320 ÷ 12 = 360

    LCM(18, 24, 60) = 360

    The pairs may be taken in any order — 24 and 60 first, then 18 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 18, 24 and 60?. The LCM of 18, 24 and 60 is 360 — 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
    182445360
    1824461,656
    1824473,384
    182448144
    1824493,528
    1824501,800
    1824511,224
    182452936
    1824533,816
    182454216
    1824553,960
    182456504
    1824571,368
    1824582,088
    1824594,248
    182460360
    1824614,392
    1824622,232
    182463504
    182464576
    1824654,680
    182466792
    1824674,824
    1824681,224
    1824691,656
    1824702,520
    1824715,112
    18247272
    1824735,256
    1824742,664

    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, 24 and 60? (The answer is: 360). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '60'), 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, 24 and 60?

    LCM of 18, 24 and 60 is 360

    How to find the LCM of 18, 24 and 60 by prime factorization?

    Take every prime that appears in 18, 24 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 18, 24 and 60 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 24 is 72, and the LCM of 72 and 60 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 18, 24 and 60?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 60 all come out whole. Any other common multiple of 18, 24 and 60 is a multiple of 360.

    See Also