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    LCM for 20, 40 and 50

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

    What's the Least Common Multiple (LCM) of 20, 40 and 50?

    Answer

    LCM of 20, 40 and 50 is
    200

    (Two hundred)

    200 is the smallest positive integer that 20, 40 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    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 factor204050Highest power
    22223223
    5555252

    LCM = 23 × 52 = 200

    Checking the LCM of 20, 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(20, 40) = (20 × 40) ÷ 20 = 800 ÷ 20 = 40

    LCM(40, 50) = (40 × 50) ÷ 10 = 2,000 ÷ 10 = 200

    LCM(20, 40, 50) = 200

    The pairs may be taken in any order — 40 and 50 first, then 20 — 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 20, 40 and 50?. The LCM of 20, 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
    203540280
    203640360
    2037401,480
    203840760
    2039401,560
    20404040
    2040411,640
    204042840
    2040431,720
    204044440
    204045360
    204046920
    2040471,880
    204048240
    2040491,960
    204050200
    2040512,040
    204052520
    2040532,120
    2040541,080
    204055440
    204056280
    2040572,280
    2040581,160
    2040592,360
    204060120
    2040612,440
    2040621,240
    2040632,520
    204064320

    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 20, 40 and 50? (The answer is: 200). Enter the first number (e.g. '20'), 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 20, 40 and 50?

    LCM of 20, 40 and 50 is 200

    How to find the LCM of 20, 40 and 50 by prime factorization?

    Take every prime that appears in 20, 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 20, 40 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 40 is 40, and the LCM of 40 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 20, 40 and 50?

    Yes, and by definition it is the smallest positive integer that is: 200 ÷ 20, 200 ÷ 40 and 200 ÷ 50 all come out whole. Any other common multiple of 20, 40 and 50 is a multiple of 200.

    See Also