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    LCM for 14, 16 and 18

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

    What's the Least Common Multiple (LCM) of 14, 16 and 18?

    Answer

    LCM of 14, 16 and 18 is
    1,008

    (One thousand eight)

    1,008 is the smallest positive integer that 14, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 14, 16 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 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

    Prime factor141618Highest power
    2224224
    3——3232
    77——7

    LCM = 24 × 32 × 7 = 1,008

    Checking the LCM of 14, 16 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(14, 16) = (14 × 16) ÷ 2 = 224 ÷ 2 = 112

    LCM(112, 18) = (112 × 18) ÷ 2 = 2,016 ÷ 2 = 1,008

    LCM(14, 16, 18) = 1,008

    The pairs may be taken in any order — 16 and 18 first, then 14 — and the answer is the same 1,008. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 14, 16 and 18?. The LCM of 14, 16 and 18 is 1,008 — 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
    31416336
    41416112
    51416560
    61416336
    71416112
    81416112
    914161,008
    101416560
    1114161,232
    121416336
    1314161,456
    141416112
    1415161,680
    141616112
    1416171,904
    1416181,008
    1416192,128
    141620560
    141621336
    1416221,232
    1416232,576
    141624336
    1416252,800
    1416261,456
    1416273,024
    141628112
    1416293,248
    1416301,680
    1416313,472
    141632224

    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 14, 16 and 18? (The answer is: 1,008). Enter the first number (e.g. '14'), the second (e.g. '16') 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 14, 16 and 18?

    LCM of 14, 16 and 18 is 1,008

    How to find the LCM of 14, 16 and 18 by prime factorization?

    Take every prime that appears in 14, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 7 = 1,008.

    Can you get the LCM of 14, 16 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 14 and 16 is 112, and the LCM of 112 and 18 is 1,008 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,008 divisible by 14, 16 and 18?

    Yes, and by definition it is the smallest positive integer that is: 1,008 ÷ 14, 1,008 ÷ 16 and 1,008 ÷ 18 all come out whole. Any other common multiple of 14, 16 and 18 is a multiple of 1,008.

    See Also