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    LCM for 12, 14 and 84

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

    What's the Least Common Multiple (LCM) of 12, 14 and 84?

    Answer

    LCM of 12, 14 and 84 is
    84

    (Eighty-four)

    84 is the smallest positive integer that 12, 14 and 84 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 14 and 84 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 84: 2 × 2 × 3 × 7 (exponent form: 22 × 3 × 7)

    Prime factor121484Highest power
    22222222
    33—33
    7—777

    LCM = 22 × 3 × 7 = 84

    Checking the LCM of 12, 14 and 84 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(12, 14) = (12 × 14) ÷ 2 = 168 ÷ 2 = 84

    LCM(84, 84) = (84 × 84) ÷ 84 = 7,056 ÷ 84 = 84

    LCM(12, 14, 84) = 84

    The pairs may be taken in any order — 14 and 84 first, then 12 — 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 12, 14 and 84?. The LCM of 12, 14 and 84 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
    1214691,932
    121470420
    1214715,964
    121472504
    1214736,132
    1214743,108
    1214752,100
    1214761,596
    121477924
    1214781,092
    1214796,636
    1214801,680
    1214812,268
    1214823,444
    1214836,972
    12148484
    1214857,140
    1214863,612
    1214872,436
    1214881,848
    1214897,476
    1214901,260
    1214911,092
    1214921,932
    1214932,604
    1214943,948
    1214957,980
    121496672
    1214978,148
    121498588

    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 12, 14 and 84? (The answer is: 84). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '84'), 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 12, 14 and 84?

    LCM of 12, 14 and 84 is 84

    How to find the LCM of 12, 14 and 84 by prime factorization?

    Take every prime that appears in 12, 14 and 84 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

    Can you get the LCM of 12, 14 and 84 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 14 is 84, and the LCM of 84 and 84 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 12, 14 and 84?

    Yes, and by definition it is the smallest positive integer that is: 84 ÷ 12, 84 ÷ 14 and 84 ÷ 84 all come out whole. Any other common multiple of 12, 14 and 84 is a multiple of 84.

    See Also