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    LCM for 25, 40 and 50

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

    What's the Least Common Multiple (LCM) of 25, 40 and 50?

    Answer

    LCM of 25, 40 and 50 is
    200

    (Two hundred)

    200 is the smallest positive integer that 25, 40 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 25, 40 and 50 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 25: 5 × 5 (exponent form: 52)

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

    All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

    Prime factor254050Highest power
    2—23223
    55255252

    LCM = 23 × 52 = 200

    Checking the LCM of 25, 40 and 50 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(25, 40) = (25 × 40) ÷ 5 = 1,000 ÷ 5 = 200

    LCM(200, 50) = (200 × 50) ÷ 50 = 10,000 ÷ 50 = 200

    LCM(25, 40, 50) = 200

    The pairs may be taken in any order — 40 and 50 first, then 25 — and the answer is the same 200. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 25, 40 and 50?. The LCM of 25, 40 and 50 is 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
    2535401,400
    2536401,800
    2537407,400
    2538403,800
    2539407,800
    254040200
    2540418,200
    2540424,200
    2540438,600
    2540442,200
    2540451,800
    2540464,600
    2540479,400
    2540481,200
    2540499,800
    254050200
    25405110,200
    2540522,600
    25405310,600
    2540545,400
    2540552,200
    2540561,400
    25405711,400
    2540585,800
    25405911,800
    254060600
    25406112,200
    2540626,200
    25406312,600
    2540641,600

    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 25, 40 and 50? (The answer is: 200). Enter the first number (e.g. '25'), the second (e.g. '40') and the third (e.g. '50'), 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 25, 40 and 50?

    LCM of 25, 40 and 50 is 200

    How to find the LCM of 25, 40 and 50 by prime factorization?

    Take every prime that appears in 25, 40 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 5² = 200.

    Can you get the LCM of 25, 40 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 25 and 40 is 200, and the LCM of 200 and 50 is 200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 200 divisible by 25, 40 and 50?

    Yes, and by definition it is the smallest positive integer that is: 200 ÷ 25, 200 ÷ 40 and 200 ÷ 50 all come out whole. Any other common multiple of 25, 40 and 50 is a multiple of 200.

    See Also