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    LCM for 9, 10 and 12

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

    What's the Least Common Multiple (LCM) of 9, 10 and 12?

    Answer

    LCM of 9, 10 and 12 is
    180

    First common multiples: 180, 360, 540, …

    180 is divisible by all three: 180 ÷ 9 = 20, 180 ÷ 10 = 18, 180 ÷ 12 = 15 — and 20, 18 and 15 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 20 and of y/10 by 18 and of z/12 by 15.

    9 = 32

    10 = 2 × 5

    12 = 22 × 3

    Prime91012Highest power
    2—22222
    332—332
    5—5—5

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

    LCM = 22 × 32 × 5 = 180

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--10--12Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--10--12">What is the LCM of 9, 10 and 12? - Calculatio</a>Copy
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    What is the LCM of 9, 10 and 12? The LCM of 9, 10 and 12 is 180 — 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--12/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 12?

    LCM of 9, 10 and 12 is 180

    How to find the LCM of 9, 10 and 12 by prime factorization?

    Take every prime that appears in 9, 10 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

    Can you get the LCM of 9, 10 and 12 two numbers at a time?

    Yes. The LCM of 9 and 10 is 90, and the LCM of 90 and 12 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 180 divisible by 9, 10 and 12?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 9, 180 ÷ 10 and 180 ÷ 12 all come out whole. Any other common multiple of 9, 10 and 12 is a multiple of 180.

    See Also