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    LCM for 14, 24 and 28

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

    What's the Least Common Multiple (LCM) of 14, 24 and 28?

    Answer

    LCM of 14, 24 and 28 is
    168

    (One hundred sixty-eight)

    168 is the smallest positive integer that 14, 24 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 14, 24 and 28 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    Prime factor142428Highest power
    22232223
    3—3—3
    77—77

    LCM = 23 × 3 × 7 = 168

    Checking the LCM of 14, 24 and 28 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, 24) = (14 × 24) ÷ 2 = 336 ÷ 2 = 168

    LCM(168, 28) = (168 × 28) ÷ 28 = 4,704 ÷ 28 = 168

    LCM(14, 24, 28) = 168

    The pairs may be taken in any order — 24 and 28 first, then 14 — and the answer is the same 168. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 14, 24 and 28?. The LCM of 14, 24 and 28 is 168 — 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
    1314242,184
    141424168
    141524840
    141624336
    1417242,856
    141824504
    1419243,192
    142024840
    142124168
    1422241,848
    1423243,864
    142424168
    1424254,200
    1424262,184
    1424271,512
    142428168
    1424294,872
    142430840
    1424315,208
    142432672
    1424331,848
    1424342,856
    142435840
    142436504
    1424376,216
    1424383,192
    1424392,184
    142440840
    1424416,888
    142442168

    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, 24 and 28? (The answer is: 168). Enter the first number (e.g. '14'), the second (e.g. '24') and the third (e.g. '28'), 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, 24 and 28?

    LCM of 14, 24 and 28 is 168

    How to find the LCM of 14, 24 and 28 by prime factorization?

    Take every prime that appears in 14, 24 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

    Can you get the LCM of 14, 24 and 28 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 14 and 24 is 168, and the LCM of 168 and 28 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 168 divisible by 14, 24 and 28?

    Yes, and by definition it is the smallest positive integer that is: 168 ÷ 14, 168 ÷ 24 and 168 ÷ 28 all come out whole. Any other common multiple of 14, 24 and 28 is a multiple of 168.

    See Also