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    LCM for 35, 40 and 120

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

    What's the Least Common Multiple (LCM) of 35, 40 and 120?

    Answer

    LCM of 35, 40 and 120 is
    840

    (Eight hundred forty)

    840 is the smallest positive integer that 35, 40 and 120 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 35, 40 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 35: 5 × 7 (exponent form: 5 × 7)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

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

    Prime factor3540120Highest power
    2—232323
    3——33
    55555
    77——7

    LCM = 23 × 3 × 5 × 7 = 840

    Checking the LCM of 35, 40 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(35, 40) = (35 × 40) ÷ 5 = 1,400 ÷ 5 = 280

    LCM(280, 120) = (280 × 120) ÷ 40 = 33,600 ÷ 40 = 840

    LCM(35, 40, 120) = 840

    The pairs may be taken in any order — 40 and 120 first, then 35 — 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 35, 40 and 120?. The LCM of 35, 40 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
    3540105840
    354010614,840
    354010729,960
    35401087,560
    354010930,520
    35401103,080
    354011131,080
    3540112560
    354011331,640
    354011415,960
    35401156,440
    35401168,120
    354011732,760
    354011816,520
    35401194,760
    3540120840
    354012133,880
    354012217,080
    354012334,440
    35401248,680
    35401257,000
    35401262,520
    354012735,560
    35401284,480
    354012936,120
    35401303,640
    354013136,680
    35401329,240
    35401335,320
    354013418,760

    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 35, 40 and 120? (The answer is: 840). Enter the first number (e.g. '35'), the second (e.g. '40') 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 35, 40 and 120?

    LCM of 35, 40 and 120 is 840

    How to find the LCM of 35, 40 and 120 by prime factorization?

    Take every prime that appears in 35, 40 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 35, 40 and 120 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 35 and 40 is 280, and the LCM of 280 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 35, 40 and 120?

    Yes, and by definition it is the smallest positive integer that is: 840 ÷ 35, 840 ÷ 40 and 840 ÷ 120 all come out whole. Any other common multiple of 35, 40 and 120 is a multiple of 840.

    See Also