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    LCM for 6, 7 and 9

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

    What's the Least Common Multiple (LCM) of 6, 7 and 9?

    Answer

    LCM of 6, 7 and 9 is
    126

    (One hundred twenty-six)

    126 is the smallest positive integer that 6, 7 and 9 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 7 and 9 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 7: 7 (exponent form: 7)

    All Prime Factors of 9: 3 × 3 (exponent form: 32)

    Prime factor679Highest power
    22——2
    33—3232
    7—7—7

    LCM = 2 × 32 × 7 = 126

    Checking the LCM of 6, 7 and 9 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, 7) = (6 × 7) ÷ 1 = 42 ÷ 1 = 42

    LCM(42, 9) = (42 × 9) ÷ 3 = 378 ÷ 3 = 126

    LCM(6, 7, 9) = 126

    The pairs may be taken in any order — 7 and 9 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, 7 and 9?. The LCM of 6, 7 and 9 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
    16742
    26742
    36742
    46784
    567210
    66742
    67742
    678168
    679126
    6710210
    6711462
    671284
    6713546
    671442
    6715210
    6716336
    6717714
    6718126
    6719798
    6720420
    672142
    6722462
    6723966
    6724168
    67251,050
    6726546
    6727378
    672884
    67291,218
    6730210

    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, 7 and 9? (The answer is: 126). Enter the first number (e.g. '6'), the second (e.g. '7') and the third (e.g. '9'), 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, 7 and 9?

    LCM of 6, 7 and 9 is 126

    How to find the LCM of 6, 7 and 9 by prime factorization?

    Take every prime that appears in 6, 7 and 9 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

    Can you get the LCM of 6, 7 and 9 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 7 is 42, and the LCM of 42 and 9 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, 7 and 9?

    Yes, and by definition it is the smallest positive integer that is: 126 ÷ 6, 126 ÷ 7 and 126 ÷ 9 all come out whole. Any other common multiple of 6, 7 and 9 is a multiple of 126.

    See Also