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    LCM for 14, 21 and 28

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

    What's the Least Common Multiple (LCM) of 14, 21 and 28?

    Answer

    LCM of 14, 21 and 28 is
    84

    (Eighty-four)

    84 is the smallest positive integer that 14, 21 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 14, 21 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 21: 3 × 7 (exponent form: 3 × 7)

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

    Prime factor142128Highest power
    22—2222
    3—3—3
    77777

    LCM = 22 × 3 × 7 = 84

    Checking the LCM of 14, 21 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, 21) = (14 × 21) ÷ 7 = 294 ÷ 7 = 42

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

    LCM(14, 21, 28) = 84

    The pairs may be taken in any order — 21 and 28 first, then 14 — and the answer is the same 84. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 14, 21 and 28?. The LCM of 14, 21 and 28 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
    131421546
    14142142
    141521210
    141621336
    141721714
    141821126
    141921798
    142021420
    14212142
    142122462
    142123966
    142124168
    1421251,050
    142126546
    142127378
    14212884
    1421291,218
    142130210
    1421311,302
    142132672
    142133462
    142134714
    142135210
    142136252
    1421371,554
    142138798
    142139546
    142140840
    1421411,722
    14214242

    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, 21 and 28? (The answer is: 84). Enter the first number (e.g. '14'), the second (e.g. '21') 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, 21 and 28?

    LCM of 14, 21 and 28 is 84

    How to find the LCM of 14, 21 and 28 by prime factorization?

    Take every prime that appears in 14, 21 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

    Can you get the LCM of 14, 21 and 28 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 14 and 21 is 42, and the LCM of 42 and 28 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, 21 and 28?

    Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 21 and 84 ÷ 28 all come out whole. Any other common multiple of 14, 21 and 28 is a multiple of 84.

    See Also