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    LCM for 3, 9 and 27

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

    What's the Least Common Multiple (LCM) of 3, 9 and 27?

    Answer

    LCM of 3, 9 and 27 is
    27

    (Twenty-seven)

    27 is the smallest positive integer that 3, 9 and 27 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 9 and 27 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 3: 3 (exponent form: 3)

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

    All Prime Factors of 27: 3 × 3 × 3 (exponent form: 33)

    Prime factor3927Highest power
    33323333

    LCM = 33 = 27

    Checking the LCM of 3, 9 and 27 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(3, 9) = (3 × 9) ÷ 3 = 27 ÷ 3 = 9

    LCM(9, 27) = (9 × 27) ÷ 9 = 243 ÷ 9 = 27

    LCM(3, 9, 27) = 27

    The pairs may be taken in any order — 9 and 27 first, then 3 — and the answer is the same 27. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 3, 9 and 27?. The LCM of 3, 9 and 27 is 27 — 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
    391236
    3913117
    3914126
    391545
    3916144
    3917153
    391818
    3919171
    3920180
    392163
    3922198
    3923207
    392472
    3925225
    3926234
    392727
    3928252
    3929261
    393090
    3931279
    3932288
    393399
    3934306
    3935315
    393636
    3937333
    3938342
    3939117
    3940360
    3941369

    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 3, 9 and 27? (The answer is: 27). Enter the first number (e.g. '3'), the second (e.g. '9') and the third (e.g. '27'), 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 3, 9 and 27?

    LCM of 3, 9 and 27 is 27

    How to find the LCM of 3, 9 and 27 by prime factorization?

    Take every prime that appears in 3, 9 and 27 to the highest power it reaches in any one of them and multiply: 3³ = 27.

    Can you get the LCM of 3, 9 and 27 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 9 is 9, and the LCM of 9 and 27 is 27 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 27 divisible by 3, 9 and 27?

    Yes, and by definition it is the smallest positive integer that is: 27 ÷ 3, 27 ÷ 9 and 27 ÷ 27 all come out whole. Any other common multiple of 3, 9 and 27 is a multiple of 27.

    See Also