Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    LCM for 3, 9 and 18

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

    What's the Least Common Multiple (LCM) of 3, 9 and 18?

    Answer

    LCM of 3, 9 and 18 is
    18

    (Eighteen)

    18 is the smallest positive integer that 3, 9 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 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 3: 3 (exponent form: 3)

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

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

    Prime factor3918Highest power
    2——22
    33323232

    LCM = 2 × 32 = 18

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

    LCM(9, 18) = (9 × 18) ÷ 9 = 162 ÷ 9 = 18

    LCM(3, 9, 18) = 18

    The pairs may be taken in any order — 9 and 18 first, then 3 — and the answer is the same 18. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/3--9--18Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/3--9--18">What is the LCM of 3, 9 and 18? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 3, 9 and 18?. The LCM of 3, 9 and 18 is 18 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/3--9--18/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    3399
    34936
    35945
    36918
    37963
    38972
    3999
    391090
    391199
    391236
    3913117
    3914126
    391545
    3916144
    3917153
    391818
    3919171
    3920180
    392163
    3922198
    3923207
    392472
    3925225
    3926234
    392727
    3928252
    3929261
    393090
    3931279
    3932288

    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 18? (The answer is: 18). Enter the first number (e.g. '3'), 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 3, 9 and 18?

    LCM of 3, 9 and 18 is 18

    How to find the LCM of 3, 9 and 18 by prime factorization?

    Take every prime that appears in 3, 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 3, 9 and 18 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 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 3, 9 and 18?

    Yes, and by definition it is the smallest positive integer that is: 18 ÷ 3, 18 ÷ 9 and 18 ÷ 18 all come out whole. Any other common multiple of 3, 9 and 18 is a multiple of 18.

    See Also