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    LCM for 8, 16 and 24

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

    What's the Least Common Multiple (LCM) of 8, 16 and 24?

    Answer

    LCM of 8, 16 and 24 is
    48

    (Forty-eight)

    48 is the smallest positive integer that 8, 16 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 16 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    Prime factor81624Highest power
    223242324
    3——33

    LCM = 24 × 3 = 48

    Checking the LCM of 8, 16 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, 16) = (8 × 16) ÷ 8 = 128 ÷ 8 = 16

    LCM(16, 24) = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

    LCM(8, 16, 24) = 48

    The pairs may be taken in any order — 16 and 24 first, then 8 — and the answer is the same 48. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 16 and 24?. The LCM of 8, 16 and 24 is 48 — 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
    8916144
    8101680
    81116176
    8121648
    81316208
    81416112
    81516240
    8161616
    81617272
    81618144
    81619304
    8162080
    81621336
    81622176
    81623368
    8162448
    81625400
    81626208
    81627432
    81628112
    81629464
    81630240
    81631496
    8163232
    81633528
    81634272
    81635560
    81636144
    81637592
    81638304

    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, 16 and 24? (The answer is: 48). Enter the first number (e.g. '8'), the second (e.g. '16') 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, 16 and 24?

    LCM of 8, 16 and 24 is 48

    How to find the LCM of 8, 16 and 24 by prime factorization?

    Take every prime that appears in 8, 16 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

    Can you get the LCM of 8, 16 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 16 is 16, and the LCM of 16 and 24 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 48 divisible by 8, 16 and 24?

    Yes, and by definition it is the smallest positive integer that is: 48 ÷ 8, 48 ÷ 16 and 48 ÷ 24 all come out whole. Any other common multiple of 8, 16 and 24 is a multiple of 48.

    See Also