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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

    (Eight hundred forty)

    840 is the smallest positive integer that 60, 84 and 120 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 60, 84 and 120 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 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

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

    All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

    Prime factor6084120Highest power
    222222323
    33333
    55—55
    7—7—7

    LCM = 23 × 3 × 5 × 7 = 840

    Checking the LCM of 60, 84 and 120 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(60, 84) = (60 × 84) ÷ 12 = 5,040 ÷ 12 = 420

    LCM(420, 120) = (420 × 120) ÷ 60 = 50,400 ÷ 60 = 840

    LCM(60, 84, 120) = 840

    The pairs may be taken in any order — 84 and 120 first, then 60 — and the answer is the same 840. That is exactly why the two routes on this page agree.

    Related Calculations

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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.
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    LCM Table

    Number 1Number 2Number 3LCM
    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

    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 60, 84 and 120? (The answer is: 840). Enter the first number (e.g. '60'), the second (e.g. '84') and the third (e.g. '120'), 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 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, and it is the check this page prints. 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