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    LCM for 15, 18 and 30

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

    What's the Least Common Multiple (LCM) of 15, 18 and 30?

    Answer

    LCM of 15, 18 and 30 is
    90

    (Ninety)

    90 is the smallest positive integer that 15, 18 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 18 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

    Prime factor151830Highest power
    2—222
    3332332
    55—55

    LCM = 2 × 32 × 5 = 90

    Checking the LCM of 15, 18 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(15, 18) = (15 × 18) ÷ 3 = 270 ÷ 3 = 90

    LCM(90, 30) = (90 × 30) ÷ 30 = 2,700 ÷ 30 = 90

    LCM(15, 18, 30) = 90

    The pairs may be taken in any order — 18 and 30 first, then 15 — and the answer is the same 90. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 18 and 30?. The LCM of 15, 18 and 30 is 90 — 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
    15151890
    151618720
    1517181,530
    15181890
    1518191,710
    151820180
    151821630
    151822990
    1518232,070
    151824360
    151825450
    1518261,170
    151827270
    1518281,260
    1518292,610
    15183090
    1518312,790
    1518321,440
    151833990
    1518341,530
    151835630
    151836180
    1518373,330
    1518381,710
    1518391,170
    151840360
    1518413,690
    151842630
    1518433,870
    1518441,980

    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 15, 18 and 30? (The answer is: 90). Enter the first number (e.g. '15'), the second (e.g. '18') 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 15, 18 and 30?

    LCM of 15, 18 and 30 is 90

    How to find the LCM of 15, 18 and 30 by prime factorization?

    Take every prime that appears in 15, 18 and 30 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 15, 18 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 18 is 90, and the LCM of 90 and 30 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 15, 18 and 30?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 15, 90 ÷ 18 and 90 ÷ 30 all come out whole. Any other common multiple of 15, 18 and 30 is a multiple of 90.

    See Also