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    LCM for 20, 50 and 75

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

    What's the Least Common Multiple (LCM) of 20, 50 and 75?

    Answer

    LCM of 20, 50 and 75 is
    300

    (Three hundred)

    300 is the smallest positive integer that 20, 50 and 75 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 50 and 75 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

    All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

    Prime factor205075Highest power
    2222—22
    3——33
    55525252

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 20, 50 and 75 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, 50) = (20 × 50) ÷ 10 = 1,000 ÷ 10 = 100

    LCM(100, 75) = (100 × 75) ÷ 25 = 7,500 ÷ 25 = 300

    LCM(20, 50, 75) = 300

    The pairs may be taken in any order — 50 and 75 first, then 20 — and the answer is the same 300. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 20, 50 and 75?. The LCM of 20, 50 and 75 is 300 — 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
    205060300
    2050616,100
    2050623,100
    2050636,300
    2050641,600
    2050651,300
    2050663,300
    2050676,700
    2050681,700
    2050696,900
    205070700
    2050717,100
    2050721,800
    2050737,300
    2050743,700
    205075300
    2050761,900
    2050777,700
    2050783,900
    2050797,900
    205080400
    2050818,100
    2050824,100
    2050838,300
    2050842,100
    2050851,700
    2050864,300
    2050878,700
    2050882,200
    2050898,900

    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, 50 and 75? (The answer is: 300). Enter the first number (e.g. '20'), the second (e.g. '50') and the third (e.g. '75'), 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, 50 and 75?

    LCM of 20, 50 and 75 is 300

    How to find the LCM of 20, 50 and 75 by prime factorization?

    Take every prime that appears in 20, 50 and 75 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 20, 50 and 75 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 50 is 100, and the LCM of 100 and 75 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 300 divisible by 20, 50 and 75?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 50 and 300 ÷ 75 all come out whole. Any other common multiple of 20, 50 and 75 is a multiple of 300.

    See Also