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    LCM for 12, 16 and 18

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

    What's the Least Common Multiple (LCM) of 12, 16 and 18?

    Answer

    LCM of 12, 16 and 18 is
    144

    First common multiples: 144, 288, 432, …

    144 is divisible by all three: 144 ÷ 12 = 12, 144 ÷ 16 = 9, 144 ÷ 18 = 8 — and 12, 9 and 8 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/12 by 12 and of y/16 by 9 and of z/18 by 8.

    12 = 22 × 3

    16 = 24

    18 = 2 × 32

    Prime121618Highest power
    22224224
    33—3232

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

    LCM = 24 × 32 = 144

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/12--16--18Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/12--16--18">What is the LCM of 12, 16 and 18? - Calculatio</a>Copy
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    What is the LCM of 12, 16 and 18? The LCM of 12, 16 and 18 is 144 — 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/12--16--18/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    3121648
    4121648
    51216240
    6121648
    71216336
    8121648
    91216144
    101216240
    111216528
    12121648
    121316624
    121416336
    121516240
    12161648
    121617816
    121618144
    121619912
    121620240
    121621336
    121622528
    1216231,104
    12162448
    1216251,200
    121626624
    121627432
    121628336
    1216291,392
    121630240
    1216311,488
    12163296

    FAQ

    What's the Least Common Multiple (LCM) of 12, 16 and 18?

    LCM of 12, 16 and 18 is 144

    How to find the LCM of 12, 16 and 18 by prime factorization?

    Take every prime that appears in 12, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

    Can you get the LCM of 12, 16 and 18 two numbers at a time?

    Yes. The LCM of 12 and 16 is 48, and the LCM of 48 and 18 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 144 divisible by 12, 16 and 18?

    Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 16 and 144 ÷ 18 all come out whole. Any other common multiple of 12, 16 and 18 is a multiple of 144.

    See Also