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    LCM for 20, 30 and 50

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

    What's the Least Common Multiple (LCM) of 20, 30 and 50?

    Answer

    LCM of 20, 30 and 50 is
    300

    (Three hundred)

    300 is the smallest positive integer that 20, 30 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 30 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

    Prime factor203050Highest power
    2222222
    3—3—3
    5555252

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 20, 30 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, 30) = (20 × 30) ÷ 10 = 600 ÷ 10 = 60

    LCM(60, 50) = (60 × 50) ÷ 10 = 3,000 ÷ 10 = 300

    LCM(20, 30, 50) = 300

    The pairs may be taken in any order — 30 and 50 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, 30 and 50?. The LCM of 20, 30 and 50 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
    203035420
    203036180
    2030372,220
    2030381,140
    203039780
    203040120
    2030412,460
    203042420
    2030432,580
    203044660
    203045180
    2030461,380
    2030472,820
    203048240
    2030492,940
    203050300
    2030511,020
    203052780
    2030533,180
    203054540
    203055660
    203056840
    2030571,140
    2030581,740
    2030593,540
    20306060
    2030613,660
    2030621,860
    2030631,260
    203064960

    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, 30 and 50? (The answer is: 300). Enter the first number (e.g. '20'), the second (e.g. '30') 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, 30 and 50?

    LCM of 20, 30 and 50 is 300

    How to find the LCM of 20, 30 and 50 by prime factorization?

    Take every prime that appears in 20, 30 and 50 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 20, 30 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 30 is 60, and the LCM of 60 and 50 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, 30 and 50?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 30 and 300 ÷ 50 all come out whole. Any other common multiple of 20, 30 and 50 is a multiple of 300.

    See Also