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    LCM for 8, 56 and 64

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

    What's the Least Common Multiple (LCM) of 8, 56 and 64?

    Answer

    LCM of 8, 56 and 64 is
    448

    (Four hundred forty-eight)

    448 is the smallest positive integer that 8, 56 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 56 and 64 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 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

    All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

    Prime factor85664Highest power
    223232626
    7—7—7

    LCM = 26 × 7 = 448

    Checking the LCM of 8, 56 and 64 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, 56) = (8 × 56) ÷ 8 = 448 ÷ 8 = 56

    LCM(56, 64) = (56 × 64) ÷ 8 = 3,584 ÷ 8 = 448

    LCM(8, 56, 64) = 448

    The pairs may be taken in any order — 56 and 64 first, then 8 — and the answer is the same 448. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 56 and 64?. The LCM of 8, 56 and 64 is 448 — 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
    84956392
    850561,400
    851562,856
    85256728
    853562,968
    854561,512
    855563,080
    8565656
    856573,192
    856581,624
    856593,304
    85660840
    856613,416
    856621,736
    85663504
    85664448
    856653,640
    856661,848
    856673,752
    85668952
    856693,864
    85670280
    856713,976
    85672504
    856734,088
    856742,072
    856754,200
    856761,064
    85677616
    856782,184

    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, 56 and 64? (The answer is: 448). Enter the first number (e.g. '8'), the second (e.g. '56') and the third (e.g. '64'), 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, 56 and 64?

    LCM of 8, 56 and 64 is 448

    How to find the LCM of 8, 56 and 64 by prime factorization?

    Take every prime that appears in 8, 56 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 7 = 448.

    Can you get the LCM of 8, 56 and 64 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 56 is 56, and the LCM of 56 and 64 is 448 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 448 divisible by 8, 56 and 64?

    Yes, and by definition it is the smallest positive integer that is: 448 ÷ 8, 448 ÷ 56 and 448 ÷ 64 all come out whole. Any other common multiple of 8, 56 and 64 is a multiple of 448.

    See Also