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    LCM for 8, 40 and 64

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

    What's the Least Common Multiple (LCM) of 8, 40 and 64?

    Answer

    LCM of 8, 40 and 64 is
    320

    (Three hundred twenty)

    320 is the smallest positive integer that 8, 40 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 40 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

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

    Prime factor84064Highest power
    223232626
    5—5—5

    LCM = 26 × 5 = 320

    Checking the LCM of 8, 40 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, 40) = (8 × 40) ÷ 8 = 320 ÷ 8 = 40

    LCM(40, 64) = (40 × 64) ÷ 8 = 2,560 ÷ 8 = 320

    LCM(8, 40, 64) = 320

    The pairs may be taken in any order — 40 and 64 first, then 8 — and the answer is the same 320. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 40 and 64?. The LCM of 8, 40 and 64 is 320 — 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
    840491,960
    84050200
    840512,040
    84052520
    840532,120
    840541,080
    84055440
    84056280
    840572,280
    840581,160
    840592,360
    84060120
    840612,440
    840621,240
    840632,520
    84064320
    84065520
    840661,320
    840672,680
    84068680
    840692,760
    84070280
    840712,840
    84072360
    840732,920
    840741,480
    84075600
    84076760
    840773,080
    840781,560

    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, 40 and 64? (The answer is: 320). Enter the first number (e.g. '8'), the second (e.g. '40') 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, 40 and 64?

    LCM of 8, 40 and 64 is 320

    How to find the LCM of 8, 40 and 64 by prime factorization?

    Take every prime that appears in 8, 40 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 5 = 320.

    Can you get the LCM of 8, 40 and 64 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 40 is 40, and the LCM of 40 and 64 is 320 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 320 divisible by 8, 40 and 64?

    Yes, and by definition it is the smallest positive integer that is: 320 ÷ 8, 320 ÷ 40 and 320 ÷ 64 all come out whole. Any other common multiple of 8, 40 and 64 is a multiple of 320.

    See Also