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    LCM for 8, 18 and 24

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

    What's the Least Common Multiple (LCM) of 8, 18 and 24?

    Answer

    LCM of 8, 18 and 24 is
    72

    (Seventy-two)

    72 is the smallest positive integer that 8, 18 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 18 and 24 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 8: 2 × 2 × 2 (exponent form: 23)

    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)

    Prime factor81824Highest power
    22322323
    3—32332

    LCM = 23 × 32 = 72

    Checking the LCM of 8, 18 and 24 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(8, 18) = (8 × 18) ÷ 2 = 144 ÷ 2 = 72

    LCM(72, 24) = (72 × 24) ÷ 24 = 1,728 ÷ 24 = 72

    LCM(8, 18, 24) = 72

    The pairs may be taken in any order — 18 and 24 first, then 8 — and the answer is the same 72. That is exactly why the two routes on this page agree.

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    What is the LCM of 8, 18 and 24?. The LCM of 8, 18 and 24 is 72 — 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
    891872
    81018360
    81118792
    8121872
    81318936
    81418504
    81518360
    81618144
    817181,224
    8181872
    818191,368
    81820360
    81821504
    81822792
    818231,656
    8182472
    818251,800
    81826936
    81827216
    81828504
    818292,088
    81830360
    818312,232
    81832288
    81833792
    818341,224
    818352,520
    8183672
    818372,664
    818381,368

    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 8, 18 and 24? (The answer is: 72). Enter the first number (e.g. '8'), the second (e.g. '18') and the third (e.g. '24'), 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 8, 18 and 24?

    LCM of 8, 18 and 24 is 72

    How to find the LCM of 8, 18 and 24 by prime factorization?

    Take every prime that appears in 8, 18 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

    Can you get the LCM of 8, 18 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 18 is 72, and the LCM of 72 and 24 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 72 divisible by 8, 18 and 24?

    Yes, and by definition it is the smallest positive integer that is: 72 ÷ 8, 72 ÷ 18 and 72 ÷ 24 all come out whole. Any other common multiple of 8, 18 and 24 is a multiple of 72.

    See Also