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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

    (Three hundred sixty)

    360 is the smallest positive integer that 18, 24 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 24 and 30 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    Prime factor182430Highest power
    2223223
    3323332
    5——55

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 18, 24 and 30 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(18, 24) = (18 × 24) ÷ 6 = 432 ÷ 6 = 72

    LCM(72, 30) = (72 × 30) ÷ 6 = 2,160 ÷ 6 = 360

    LCM(18, 24, 30) = 360

    The pairs may be taken in any order — 24 and 30 first, then 18 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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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.
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    LCM Table

    Number 1Number 2Number 3LCM
    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

    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 18, 24 and 30? (The answer is: 360). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '30'), 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 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, and it is the check this page prints. 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