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    LCM for 8, 9 and 10

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

    What's the Least Common Multiple (LCM) of 8, 9 and 10?

    Answer

    LCM of 8, 9 and 10 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 8, 9 and 10 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 9 and 10 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 9: 3 × 3 (exponent form: 32)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

    Prime factor8910Highest power
    223—223
    3—32—32
    5——55

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 8, 9 and 10 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, 9) = (8 × 9) ÷ 1 = 72 ÷ 1 = 72

    LCM(72, 10) = (72 × 10) ÷ 2 = 720 ÷ 2 = 360

    LCM(8, 9, 10) = 360

    The pairs may be taken in any order — 9 and 10 first, then 8 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 9 and 10?. The LCM of 8, 9 and 10 is 360 — 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
    18972
    28972
    38972
    48972
    589360
    68972
    789504
    88972
    89972
    8910360
    8911792
    891272
    8913936
    8914504
    8915360
    8916144
    89171,224
    891872
    89191,368
    8920360
    8921504
    8922792
    89231,656
    892472
    89251,800
    8926936
    8927216
    8928504
    89292,088
    8930360

    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, 9 and 10? (The answer is: 360). Enter the first number (e.g. '8'), the second (e.g. '9') and the third (e.g. '10'), 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, 9 and 10?

    LCM of 8, 9 and 10 is 360

    How to find the LCM of 8, 9 and 10 by prime factorization?

    Take every prime that appears in 8, 9 and 10 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 8, 9 and 10 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 9 is 72, and the LCM of 72 and 10 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 8, 9 and 10?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 9 and 360 ÷ 10 all come out whole. Any other common multiple of 8, 9 and 10 is a multiple of 360.

    See Also