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    LCM for 16, 40 and 56

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

    What's the Least Common Multiple (LCM) of 16, 40 and 56?

    Answer

    LCM of 16, 40 and 56 is
    560

    (Five hundred sixty)

    560 is the smallest positive integer that 16, 40 and 56 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 40 and 56 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    All Prime Factors of 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

    Prime factor164056Highest power
    224232324
    5—5—5
    7——77

    LCM = 24 × 5 × 7 = 560

    Checking the LCM of 16, 40 and 56 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(16, 40) = (16 × 40) ÷ 8 = 640 ÷ 8 = 80

    LCM(80, 56) = (80 × 56) ÷ 8 = 4,480 ÷ 8 = 560

    LCM(16, 40, 56) = 560

    The pairs may be taken in any order — 40 and 56 first, then 16 — and the answer is the same 560. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 16, 40 and 56?. The LCM of 16, 40 and 56 is 560 — 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
    1640413,280
    1640421,680
    1640433,440
    164044880
    164045720
    1640461,840
    1640473,760
    164048240
    1640493,920
    164050400
    1640514,080
    1640521,040
    1640534,240
    1640542,160
    164055880
    164056560
    1640574,560
    1640582,320
    1640594,720
    164060240
    1640614,880
    1640622,480
    1640635,040
    164064320
    1640651,040
    1640662,640
    1640675,360
    1640681,360
    1640695,520
    164070560

    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 16, 40 and 56? (The answer is: 560). Enter the first number (e.g. '16'), the second (e.g. '40') and the third (e.g. '56'), 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 16, 40 and 56?

    LCM of 16, 40 and 56 is 560

    How to find the LCM of 16, 40 and 56 by prime factorization?

    Take every prime that appears in 16, 40 and 56 to the highest power it reaches in any one of them and multiply: 2⁴ × 5 × 7 = 560.

    Can you get the LCM of 16, 40 and 56 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 40 is 80, and the LCM of 80 and 56 is 560 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 560 divisible by 16, 40 and 56?

    Yes, and by definition it is the smallest positive integer that is: 560 ÷ 16, 560 ÷ 40 and 560 ÷ 56 all come out whole. Any other common multiple of 16, 40 and 56 is a multiple of 560.

    See Also