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    LCM for 8, 21 and 24

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

    What's the Least Common Multiple (LCM) of 8, 21 and 24?

    Answer

    LCM of 8, 21 and 24 is
    168

    (One hundred sixty-eight)

    168 is the smallest positive integer that 8, 21 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 21 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 21: 3 × 7 (exponent form: 3 × 7)

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

    Prime factor82124Highest power
    223—2323
    3—333
    7—7—7

    LCM = 23 × 3 × 7 = 168

    Checking the LCM of 8, 21 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, 21) = (8 × 21) ÷ 1 = 168 ÷ 1 = 168

    LCM(168, 24) = (168 × 24) ÷ 24 = 4,032 ÷ 24 = 168

    LCM(8, 21, 24) = 168

    The pairs may be taken in any order — 21 and 24 first, then 8 — and the answer is the same 168. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 21 and 24?. The LCM of 8, 21 and 24 is 168 — 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
    8921504
    81021840
    811211,848
    81221168
    813212,184
    81421168
    81521840
    81621336
    817212,856
    81821504
    819213,192
    82021840
    82121168
    821221,848
    821233,864
    82124168
    821254,200
    821262,184
    821271,512
    82128168
    821294,872
    82130840
    821315,208
    82132672
    821331,848
    821342,856
    82135840
    82136504
    821376,216
    821383,192

    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, 21 and 24? (The answer is: 168). Enter the first number (e.g. '8'), the second (e.g. '21') 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, 21 and 24?

    LCM of 8, 21 and 24 is 168

    How to find the LCM of 8, 21 and 24 by prime factorization?

    Take every prime that appears in 8, 21 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

    Can you get the LCM of 8, 21 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 21 is 168, and the LCM of 168 and 24 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 168 divisible by 8, 21 and 24?

    Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 21 and 168 ÷ 24 all come out whole. Any other common multiple of 8, 21 and 24 is a multiple of 168.

    See Also