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    LCM for 7, 8 and 28

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

    What's the Least Common Multiple (LCM) of 7, 8 and 28?

    Answer

    LCM of 7, 8 and 28 is
    56

    (Fifty-six)

    56 is the smallest positive integer that 7, 8 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 8 and 28 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 7: 7 (exponent form: 7)

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    Prime factor7828Highest power
    2—232223
    77—77

    LCM = 23 × 7 = 56

    Checking the LCM of 7, 8 and 28 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(7, 8) = (7 × 8) ÷ 1 = 56 ÷ 1 = 56

    LCM(56, 28) = (56 × 28) ÷ 28 = 1,568 ÷ 28 = 56

    LCM(7, 8, 28) = 56

    The pairs may be taken in any order — 8 and 28 first, then 7 — and the answer is the same 56. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 7, 8 and 28?. The LCM of 7, 8 and 28 is 56 — 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
    7813728
    781456
    7815840
    7816112
    7817952
    7818504
    78191,064
    7820280
    7821168
    7822616
    78231,288
    7824168
    78251,400
    7826728
    78271,512
    782856
    78291,624
    7830840
    78311,736
    7832224
    78331,848
    7834952
    7835280
    7836504
    78372,072
    78381,064
    78392,184
    7840280
    78412,296
    7842168

    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 7, 8 and 28? (The answer is: 56). Enter the first number (e.g. '7'), the second (e.g. '8') and the third (e.g. '28'), 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 7, 8 and 28?

    LCM of 7, 8 and 28 is 56

    How to find the LCM of 7, 8 and 28 by prime factorization?

    Take every prime that appears in 7, 8 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

    Can you get the LCM of 7, 8 and 28 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 8 is 56, and the LCM of 56 and 28 is 56 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 56 divisible by 7, 8 and 28?

    Yes, and by definition it is the smallest positive integer that is: 56 ÷ 7, 56 ÷ 8 and 56 ÷ 28 all come out whole. Any other common multiple of 7, 8 and 28 is a multiple of 56.

    See Also