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    LCM for 9, 10 and 15

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

    What's the Least Common Multiple (LCM) of 9, 10 and 15?

    Answer

    LCM of 9, 10 and 15 is
    90

    First common multiples: 90, 180, 270, …

    90 is divisible by all three: 90 ÷ 9 = 10, 90 ÷ 10 = 9, 90 ÷ 15 = 6 — and 10, 9 and 6 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/9 by 10 and of y/10 by 9 and of z/15 by 6.

    9 = 32

    10 = 2 × 5

    15 = 3 × 5

    Prime91015Highest power
    2—2—2
    332—332
    5—555

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 2 × 32 × 5 = 90

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--10--15Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--10--15">What is the LCM of 9, 10 and 15? - Calculatio</a>Copy
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    What is the LCM of 9, 10 and 15? The LCM of 9, 10 and 15 is 90 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--10--15/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    191090
    291090
    391090
    4910180
    591090
    691090
    7910630
    8910360
    991090
    9101090
    91011990
    91012180
    910131,170
    91014630
    9101590
    91016720
    910171,530
    9101890
    910191,710
    91020180
    91021630
    91022990
    910232,070
    91024360
    91025450
    910261,170
    91027270
    910281,260
    910292,610
    9103090

    FAQ

    What's the Least Common Multiple (LCM) of 9, 10 and 15?

    LCM of 9, 10 and 15 is 90

    How to find the LCM of 9, 10 and 15 by prime factorization?

    Take every prime that appears in 9, 10 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 9, 10 and 15 two numbers at a time?

    Yes. The LCM of 9 and 10 is 90, and the LCM of 90 and 15 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 9, 10 and 15?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 9, 90 ÷ 10 and 90 ÷ 15 all come out whole. Any other common multiple of 9, 10 and 15 is a multiple of 90.

    See Also