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    LCM for 5, 8 and 9

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

    What's the Least Common Multiple (LCM) of 5, 8 and 9?

    Answer

    LCM of 5, 8 and 9 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 5, 8 and 9 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 5, 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 5: 5 (exponent form: 5)

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

    All Prime Factors of 9: 3 × 3 (exponent form: 32)

    Prime factor589Highest power
    2—23—23
    3——3232
    55——5

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 5, 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(5, 8) = (5 × 8) ÷ 1 = 40 ÷ 1 = 40

    LCM(40, 9) = (40 × 9) ÷ 1 = 360 ÷ 1 = 360

    LCM(5, 8, 9) = 360

    The pairs may be taken in any order — 8 and 9 first, then 5 — 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 5, 8 and 9?. The LCM of 5, 8 and 9 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
    15840
    25840
    358120
    45840
    55840
    568120
    578280
    58840
    589360
    581040
    5811440
    5812120
    5813520
    5814280
    5815120
    581680
    5817680
    5818360
    5819760
    582040
    5821840
    5822440
    5823920
    5824120
    5825200
    5826520
    58271,080
    5828280
    58291,160
    5830120

    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 5, 8 and 9? (The answer is: 360). Enter the first number (e.g. '5'), 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 5, 8 and 9?

    LCM of 5, 8 and 9 is 360

    How to find the LCM of 5, 8 and 9 by prime factorization?

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

    Can you get the LCM of 5, 8 and 9 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 5 and 8 is 40, and the LCM of 40 and 9 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 5, 8 and 9?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 5, 360 ÷ 8 and 360 ÷ 9 all come out whole. Any other common multiple of 5, 8 and 9 is a multiple of 360.

    See Also