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    LCM for 60, 84 and 120

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

    What's the Least Common Multiple (LCM) of 60, 84 and 120?

    Answer

    LCM of 60, 84 and 120 is
    840

    First common multiples: 840; 1,680; 2,520; …

    840 is divisible by all three: 840 ÷ 60 = 14, 840 ÷ 84 = 10, 840 ÷ 120 = 7 — and 14, 10 and 7 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/60 by 14 and of y/84 by 10 and of z/120 by 7.

    60 = 22 × 3 × 5

    84 = 22 × 3 × 7

    120 = 23 × 3 × 5

    Prime6084120Highest power
    222222323
    33333
    55—55
    7—7—7

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

    LCM = 23 × 3 × 5 × 7 = 840

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/60--84--120Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/60--84--120">What is the LCM of 60, 84 and 120? - Calculatio</a>Copy
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    What is the LCM of 60, 84 and 120? The LCM of 60, 84 and 120 is 840 — 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/60--84--120/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    6084105420
    608410622,260
    608410744,940
    60841083,780
    608410945,780
    60841104,620
    608411115,540
    60841121,680
    608411347,460
    60841147,980
    60841159,660
    608411612,180
    608411716,380
    608411824,780
    60841197,140
    6084120840
    608412150,820
    608412225,620
    608412317,220
    608412413,020
    608412510,500
    60841261,260
    608412753,340
    608412813,440
    608412918,060
    60841305,460
    608413155,020
    60841324,620
    60841337,980
    608413428,140

    FAQ

    What's the Least Common Multiple (LCM) of 60, 84 and 120?

    LCM of 60, 84 and 120 is 840

    How to find the LCM of 60, 84 and 120 by prime factorization?

    Take every prime that appears in 60, 84 and 120 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

    Can you get the LCM of 60, 84 and 120 two numbers at a time?

    Yes. The LCM of 60 and 84 is 420, and the LCM of 420 and 120 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 840 divisible by 60, 84 and 120?

    Yes, and by definition it is the smallest positive integer that is: 840 ÷ 60, 840 ÷ 84 and 840 ÷ 120 all come out whole. Any other common multiple of 60, 84 and 120 is a multiple of 840.

    See Also