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    LCM for 50, 56 and 105

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

    What's the Least Common Multiple (LCM) of 50, 56 and 105?

    Answer

    LCM of 50, 56 and 105 is
    4,200

    (Four thousand two hundred)

    4,200 is the smallest positive integer that 50, 56 and 105 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 50, 56 and 105 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

    All Prime Factors of 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

    All Prime Factors of 105: 3 × 5 × 7 (exponent form: 3 × 5 × 7)

    Prime factor5056105Highest power
    2223—23
    3——33
    552—552
    7—777

    LCM = 23 × 3 × 52 × 7 = 4,200

    Checking the LCM of 50, 56 and 105 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(50, 56) = (50 × 56) ÷ 2 = 2,800 ÷ 2 = 1,400

    LCM(1,400, 105) = (1,400 × 105) ÷ 35 = 147,000 ÷ 35 = 4,200

    LCM(50, 56, 105) = 4,200

    The pairs may be taken in any order — 56 and 105 first, then 50 — and the answer is the same 4,200. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 50, 56 and 105?. The LCM of 50, 56 and 105 is 4,200 — 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
    50569012,600
    50569118,200
    50569232,200
    505693130,200
    50569465,800
    50569526,600
    50569616,800
    505697135,800
    5056989,800
    505699138,600
    50561001,400
    5056101141,400
    505610271,400
    5056103144,200
    505610418,200
    50561054,200
    505610674,200
    5056107149,800
    505610837,800
    5056109152,600
    505611015,400
    5056111155,400
    50561122,800
    5056113158,200
    505611479,800
    505611532,200
    505611640,600
    5056117163,800
    505611882,600
    505611923,800

    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 50, 56 and 105? (The answer is: 4,200). Enter the first number (e.g. '50'), the second (e.g. '56') and the third (e.g. '105'), 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 50, 56 and 105?

    LCM of 50, 56 and 105 is 4,200

    How to find the LCM of 50, 56 and 105 by prime factorization?

    Take every prime that appears in 50, 56 and 105 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² × 7 = 4,200.

    Can you get the LCM of 50, 56 and 105 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 50 and 56 is 1,400, and the LCM of 1,400 and 105 is 4,200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 4,200 divisible by 50, 56 and 105?

    Yes, and by definition it is the smallest positive integer that is: 4,200 ÷ 50, 4,200 ÷ 56 and 4,200 ÷ 105 all come out whole. Any other common multiple of 50, 56 and 105 is a multiple of 4,200.

    See Also