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    LCM for 6, 9 and 18

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

    What's the Least Common Multiple (LCM) of 6, 9 and 18?

    Answer

    LCM of 6, 9 and 18 is
    18

    (Eighteen)

    18 is the smallest positive integer that 6, 9 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 9 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 9: 3 × 3 (exponent form: 32)

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

    Prime factor6918Highest power
    22—22
    33323232

    LCM = 2 × 32 = 18

    Checking the LCM of 6, 9 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, 9) = (6 × 9) ÷ 3 = 54 ÷ 3 = 18

    LCM(18, 18) = (18 × 18) ÷ 18 = 324 ÷ 18 = 18

    LCM(6, 9, 18) = 18

    The pairs may be taken in any order — 9 and 18 first, then 6 — and the answer is the same 18. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 6, 9 and 18?. The LCM of 6, 9 and 18 is 18 — 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
    36918
    46936
    56990
    66918
    679126
    68972
    69918
    691090
    6911198
    691236
    6913234
    6914126
    691590
    6916144
    6917306
    691818
    6919342
    6920180
    6921126
    6922198
    6923414
    692472
    6925450
    6926234
    692754
    6928252
    6929522
    693090
    6931558
    6932288

    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, 9 and 18? (The answer is: 18). Enter the first number (e.g. '6'), the second (e.g. '9') 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, 9 and 18?

    LCM of 6, 9 and 18 is 18

    How to find the LCM of 6, 9 and 18 by prime factorization?

    Take every prime that appears in 6, 9 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² = 18.

    Can you get the LCM of 6, 9 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 9 is 18, and the LCM of 18 and 18 is 18 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 18 divisible by 6, 9 and 18?

    Yes, and by definition it is the smallest positive integer that is: 18 ÷ 6, 18 ÷ 9 and 18 ÷ 18 all come out whole. Any other common multiple of 6, 9 and 18 is a multiple of 18.

    See Also