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    LCM for 5, 9 and 10

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

    What's the Least Common Multiple (LCM) of 5, 9 and 10?

    Answer

    LCM of 5, 9 and 10 is
    90

    (Ninety)

    90 is the smallest positive integer that 5, 9 and 10 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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

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

    Prime factor5910Highest power
    2——22
    3—32—32
    55—55

    LCM = 2 × 32 × 5 = 90

    Checking the LCM of 5, 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(5, 9) = (5 × 9) ÷ 1 = 45 ÷ 1 = 45

    LCM(45, 10) = (45 × 10) ÷ 5 = 450 ÷ 5 = 90

    LCM(5, 9, 10) = 90

    The pairs may be taken in any order — 9 and 10 first, then 5 — and the answer is the same 90. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 5, 9 and 10?. The LCM of 5, 9 and 10 is 90 — 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
    15945
    25990
    35945
    459180
    55945
    56990
    579315
    589360
    59945
    591090
    5911495
    5912180
    5913585
    5914630
    591545
    5916720
    5917765
    591890
    5919855
    5920180
    5921315
    5922990
    59231,035
    5924360
    5925225
    59261,170
    5927135
    59281,260
    59291,305
    593090

    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, 9 and 10? (The answer is: 90). Enter the first number (e.g. '5'), 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 5, 9 and 10?

    LCM of 5, 9 and 10 is 90

    How to find the LCM of 5, 9 and 10 by prime factorization?

    Take every prime that appears in 5, 9 and 10 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 5, 9 and 10 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 5 and 9 is 45, and the LCM of 45 and 10 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 90 divisible by 5, 9 and 10?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 5, 90 ÷ 9 and 90 ÷ 10 all come out whole. Any other common multiple of 5, 9 and 10 is a multiple of 90.

    See Also