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    LCM for 8, 24 and 48

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

    What's the Least Common Multiple (LCM) of 8, 24 and 48?

    Answer

    LCM of 8, 24 and 48 is
    48

    (Forty-eight)

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

    Finding the LCM of 8, 24 and 48 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor82448Highest power
    223232424
    3—333

    LCM = 24 × 3 = 48

    Checking the LCM of 8, 24 and 48 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, 24) = (8 × 24) ÷ 8 = 192 ÷ 8 = 24

    LCM(24, 48) = (24 × 48) ÷ 24 = 1,152 ÷ 24 = 48

    LCM(8, 24, 48) = 48

    The pairs may be taken in any order — 24 and 48 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, 24 and 48?. The LCM of 8, 24 and 48 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
    82433264
    82434408
    82435840
    8243672
    82437888
    82438456
    82439312
    82440120
    82441984
    82442168
    824431,032
    82444264
    82445360
    82446552
    824471,128
    8244848
    824491,176
    82450600
    82451408
    82452312
    824531,272
    82454216
    824551,320
    82456168
    82457456
    82458696
    824591,416
    82460120
    824611,464
    82462744

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

    LCM of 8, 24 and 48 is 48

    How to find the LCM of 8, 24 and 48 by prime factorization?

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

    Can you get the LCM of 8, 24 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 24 is 24, and the LCM of 24 and 48 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, 24 and 48?

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

    See Also