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    LCM for 18, 24 and 30

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

    What's the Least Common Multiple (LCM) of 18, 24 and 30?

    Answer

    LCM of 18, 24 and 30 is
    360

    First common multiples: 360; 720; 1,080; …

    360 is divisible by all three: 360 ÷ 18 = 20, 360 ÷ 24 = 15, 360 ÷ 30 = 12 — and 20, 15 and 12 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/18 by 20 and of y/24 by 15 and of z/30 by 12.

    18 = 2 × 32

    24 = 23 × 3

    30 = 2 × 3 × 5

    Prime182430Highest power
    2223223
    3323332
    5——55

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

    LCM = 23 × 32 × 5 = 360

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/18--24--30Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/18--24--30">What is the LCM of 18, 24 and 30? - Calculatio</a>Copy
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    What is the LCM of 18, 24 and 30? The LCM of 18, 24 and 30 is 360 — 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/18--24--30/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    151824360
    161824144
    1718241,224
    18182472
    1819241,368
    182024360
    182124504
    182224792
    1823241,656
    18242472
    1824251,800
    182426936
    182427216
    182428504
    1824292,088
    182430360
    1824312,232
    182432288
    182433792
    1824341,224
    1824352,520
    18243672
    1824372,664
    1824381,368
    182439936
    182440360
    1824412,952
    182442504
    1824433,096
    182444792

    FAQ

    What's the Least Common Multiple (LCM) of 18, 24 and 30?

    LCM of 18, 24 and 30 is 360

    How to find the LCM of 18, 24 and 30 by prime factorization?

    Take every prime that appears in 18, 24 and 30 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 18, 24 and 30 two numbers at a time?

    Yes. The LCM of 18 and 24 is 72, and the LCM of 72 and 30 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 18, 24 and 30?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 18, 360 ÷ 24 and 360 ÷ 30 all come out whole. Any other common multiple of 18, 24 and 30 is a multiple of 360.

    See Also