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    LCM for 6, 14 and 18

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

    What's the Least Common Multiple (LCM) of 6, 14 and 18?

    Answer

    LCM of 6, 14 and 18 is
    126

    (One hundred twenty-six)

    126 is the smallest positive integer that 6, 14 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 14 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 14: 2 × 7 (exponent form: 2 × 7)

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

    Prime factor61418Highest power
    22222
    33—3232
    7—7—7

    LCM = 2 × 32 × 7 = 126

    Checking the LCM of 6, 14 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, 14) = (6 × 14) ÷ 2 = 84 ÷ 2 = 42

    LCM(42, 18) = (42 × 18) ÷ 6 = 756 ÷ 6 = 126

    LCM(6, 14, 18) = 126

    The pairs may be taken in any order — 14 and 18 first, then 6 — and the answer is the same 126. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 6, 14 and 18?. The LCM of 6, 14 and 18 is 126 — 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
    361442
    461484
    5614210
    661442
    671442
    6814168
    6914126
    61014210
    61114462
    6121484
    61314546
    6141442
    61415210
    61416336
    61417714
    61418126
    61419798
    61420420
    6142142
    61422462
    61423966
    61424168
    614251,050
    61426546
    61427378
    6142884
    614291,218
    61430210
    614311,302
    61432672

    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, 14 and 18? (The answer is: 126). Enter the first number (e.g. '6'), the second (e.g. '14') 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, 14 and 18?

    LCM of 6, 14 and 18 is 126

    How to find the LCM of 6, 14 and 18 by prime factorization?

    Take every prime that appears in 6, 14 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

    Can you get the LCM of 6, 14 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 14 is 42, and the LCM of 42 and 18 is 126 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 126 divisible by 6, 14 and 18?

    Yes, and by definition it is the smallest positive integer that is: 126 ÷ 6, 126 ÷ 14 and 126 ÷ 18 all come out whole. Any other common multiple of 6, 14 and 18 is a multiple of 126.

    See Also