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    LCM for 12, 30 and 84

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

    What's the Least Common Multiple (LCM) of 12, 30 and 84?

    Answer

    LCM of 12, 30 and 84 is
    420

    First common multiples: 420; 840; 1,260; …

    420 is divisible by all three: 420 ÷ 12 = 35, 420 ÷ 30 = 14, 420 ÷ 84 = 5 — and 35, 14 and 5 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/12 by 35 and of y/30 by 14 and of z/84 by 5.

    12 = 22 × 3

    30 = 2 × 3 × 5

    84 = 22 × 3 × 7

    Prime123084Highest power
    22222222
    33333
    5—5—5
    7——77

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 22 × 3 × 5 × 7 = 420

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/12--30--84Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/12--30--84">What is the LCM of 12, 30 and 84? - Calculatio</a>Copy
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    What is the LCM of 12, 30 and 84? The LCM of 12, 30 and 84 is 420 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/12--30--84/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    1230691,380
    123070420
    1230714,260
    123072360
    1230734,380
    1230742,220
    123075300
    1230761,140
    1230774,620
    123078780
    1230794,740
    123080240
    1230811,620
    1230822,460
    1230834,980
    123084420
    1230851,020
    1230862,580
    1230871,740
    1230881,320
    1230895,340
    123090180
    1230915,460
    1230921,380
    1230931,860
    1230942,820
    1230951,140
    123096480
    1230975,820
    1230982,940

    FAQ

    What's the Least Common Multiple (LCM) of 12, 30 and 84?

    LCM of 12, 30 and 84 is 420

    How to find the LCM of 12, 30 and 84 by prime factorization?

    Take every prime that appears in 12, 30 and 84 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

    Can you get the LCM of 12, 30 and 84 two numbers at a time?

    Yes. The LCM of 12 and 30 is 60, and the LCM of 60 and 84 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 420 divisible by 12, 30 and 84?

    Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 30 and 420 ÷ 84 all come out whole. Any other common multiple of 12, 30 and 84 is a multiple of 420.

    See Also