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    LCM for 7, 8 and 9

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

    What's the Least Common Multiple (LCM) of 7, 8 and 9?

    Answer

    LCM of 7, 8 and 9 is
    504

    (Five hundred four)

    504 is the smallest positive integer that 7, 8 and 9 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 8 and 9 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 9: 3 × 3 (exponent form: 32)

    Prime factor789Highest power
    2—23—23
    3——3232
    77——7

    LCM = 23 × 32 × 7 = 504

    Checking the LCM of 7, 8 and 9 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, 9) = (56 × 9) ÷ 1 = 504 ÷ 1 = 504

    LCM(7, 8, 9) = 504

    The pairs may be taken in any order — 8 and 9 first, then 7 — and the answer is the same 504. 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 9?. The LCM of 7, 8 and 9 is 504 — 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
    17856
    27856
    378168
    47856
    578280
    678168
    77856
    78856
    789504
    7810280
    7811616
    7812168
    7813728
    781456
    7815840
    7816112
    7817952
    7818504
    78191,064
    7820280
    7821168
    7822616
    78231,288
    7824168
    78251,400
    7826728
    78271,512
    782856
    78291,624
    7830840

    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 9? (The answer is: 504). Enter the first number (e.g. '7'), the second (e.g. '8') and the third (e.g. '9'), 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 9?

    LCM of 7, 8 and 9 is 504

    How to find the LCM of 7, 8 and 9 by prime factorization?

    Take every prime that appears in 7, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 7 = 504.

    Can you get the LCM of 7, 8 and 9 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 9 is 504 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 504 divisible by 7, 8 and 9?

    Yes, and by definition it is the smallest positive integer that is: 504 ÷ 7, 504 ÷ 8 and 504 ÷ 9 all come out whole. Any other common multiple of 7, 8 and 9 is a multiple of 504.

    See Also