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    LCM for 14, 28 and 42

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

    What's the Least Common Multiple (LCM) of 14, 28 and 42?

    Answer

    LCM of 14, 28 and 42 is
    84

    (Eighty-four)

    84 is the smallest positive integer that 14, 28 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 14, 28 and 42 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

    All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

    Prime factor142842Highest power
    2222222
    3——33
    77777

    LCM = 22 × 3 × 7 = 84

    Checking the LCM of 14, 28 and 42 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, 28) = (14 × 28) ÷ 14 = 392 ÷ 14 = 28

    LCM(28, 42) = (28 × 42) ÷ 14 = 1,176 ÷ 14 = 84

    LCM(14, 28, 42) = 84

    The pairs may be taken in any order — 28 and 42 first, then 14 — and the answer is the same 84. 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, 28 and 42?. The LCM of 14, 28 and 42 is 84 — 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
    142728756
    14282828
    142829812
    142830420
    142831868
    142832224
    142833924
    142834476
    142835140
    142836252
    1428371,036
    142838532
    1428391,092
    142840280
    1428411,148
    14284284
    1428431,204
    142844308
    1428451,260
    142846644
    1428471,316
    142848336
    142849196
    142850700
    1428511,428
    142852364
    1428531,484
    142854756
    1428551,540
    14285656

    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, 28 and 42? (The answer is: 84). Enter the first number (e.g. '14'), the second (e.g. '28') and the third (e.g. '42'), 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, 28 and 42?

    LCM of 14, 28 and 42 is 84

    How to find the LCM of 14, 28 and 42 by prime factorization?

    Take every prime that appears in 14, 28 and 42 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

    Can you get the LCM of 14, 28 and 42 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 14 and 28 is 28, and the LCM of 28 and 42 is 84 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 84 divisible by 14, 28 and 42?

    Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 28 and 84 ÷ 42 all come out whole. Any other common multiple of 14, 28 and 42 is a multiple of 84.

    See Also