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    LCM for 6, 15 and 18

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

    What's the Least Common Multiple (LCM) of 6, 15 and 18?

    Answer

    LCM of 6, 15 and 18 is
    90

    (Ninety)

    90 is the smallest positive integer that 6, 15 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 15 and 18 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 6: 2 × 3 (exponent form: 2 × 3)

    All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

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

    Prime factor61518Highest power
    22—22
    3333232
    5—5—5

    LCM = 2 × 32 × 5 = 90

    Checking the LCM of 6, 15 and 18 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(6, 15) = (6 × 15) ÷ 3 = 90 ÷ 3 = 30

    LCM(30, 18) = (30 × 18) ÷ 6 = 540 ÷ 6 = 90

    LCM(6, 15, 18) = 90

    The pairs may be taken in any order — 15 and 18 first, then 6 — 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 6, 15 and 18?. The LCM of 6, 15 and 18 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
    361530
    461560
    561530
    661530
    6715210
    6815120
    691590
    6101530
    61115330
    6121560
    61315390
    61415210
    6151530
    61516240
    61517510
    6151890
    61519570
    6152060
    61521210
    61522330
    61523690
    61524120
    61525150
    61526390
    61527270
    61528420
    61529870
    6153030
    61531930
    61532480

    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 6, 15 and 18? (The answer is: 90). Enter the first number (e.g. '6'), the second (e.g. '15') and the third (e.g. '18'), 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 6, 15 and 18?

    LCM of 6, 15 and 18 is 90

    How to find the LCM of 6, 15 and 18 by prime factorization?

    Take every prime that appears in 6, 15 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 6, 15 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 15 is 30, and the LCM of 30 and 18 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 6, 15 and 18?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 6, 90 ÷ 15 and 90 ÷ 18 all come out whole. Any other common multiple of 6, 15 and 18 is a multiple of 90.

    See Also