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    LCM for 6, 11 and 18

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

    What's the Least Common Multiple (LCM) of 6, 11 and 18?

    Answer

    LCM of 6, 11 and 18 is
    198

    (One hundred ninety-eight)

    198 is the smallest positive integer that 6, 11 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 11 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 11: 11 (exponent form: 11)

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

    Prime factor61118Highest power
    22—22
    33—3232
    11—11—11

    LCM = 2 × 32 × 11 = 198

    Checking the LCM of 6, 11 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, 11) = (6 × 11) ÷ 1 = 66 ÷ 1 = 66

    LCM(66, 18) = (66 × 18) ÷ 6 = 1,188 ÷ 6 = 198

    LCM(6, 11, 18) = 198

    The pairs may be taken in any order — 11 and 18 first, then 6 — and the answer is the same 198. That is exactly why the two routes on this page agree.

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    What is the LCM of 6, 11 and 18?. The LCM of 6, 11 and 18 is 198 — 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
    361166
    4611132
    5611330
    661166
    6711462
    6811264
    6911198
    61011330
    6111166
    61112132
    61113858
    61114462
    61115330
    61116528
    611171,122
    61118198
    611191,254
    61120660
    61121462
    6112266
    611231,518
    61124264
    611251,650
    61126858
    61127594
    61128924
    611291,914
    61130330
    611312,046
    611321,056

    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, 11 and 18? (The answer is: 198). Enter the first number (e.g. '6'), the second (e.g. '11') 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, 11 and 18?

    LCM of 6, 11 and 18 is 198

    How to find the LCM of 6, 11 and 18 by prime factorization?

    Take every prime that appears in 6, 11 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 11 = 198.

    Can you get the LCM of 6, 11 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 11 is 66, and the LCM of 66 and 18 is 198 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 198 divisible by 6, 11 and 18?

    Yes, and by definition it is the smallest positive integer that is: 198 ÷ 6, 198 ÷ 11 and 198 ÷ 18 all come out whole. Any other common multiple of 6, 11 and 18 is a multiple of 198.

    See Also