Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    LCM for 20, 25 and 30

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

    What's the Least Common Multiple (LCM) of 20, 25 and 30?

    Answer

    LCM of 20, 25 and 30 is
    300

    (Three hundred)

    300 is the smallest positive integer that 20, 25 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 25 and 30 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 25: 5 × 5 (exponent form: 52)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    Prime factor202530Highest power
    222—222
    3——33
    5552552

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 20, 25 and 30 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, 25) = (20 × 25) ÷ 5 = 500 ÷ 5 = 100

    LCM(100, 30) = (100 × 30) ÷ 10 = 3,000 ÷ 10 = 300

    LCM(20, 25, 30) = 300

    The pairs may be taken in any order — 25 and 30 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

    Share This Calculation
    Print
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--25--30Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--25--30">What is the LCM of 20, 25 and 30? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 20, 25 and 30?. The LCM of 20, 25 and 30 is 300 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--25--30/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    152025300
    162025400
    1720251,700
    182025900
    1920251,900
    202025100
    2021252,100
    2022251,100
    2023252,300
    202425600
    202525100
    2025261,300
    2025272,700
    202528700
    2025292,900
    202530300
    2025313,100
    202532800
    2025333,300
    2025341,700
    202535700
    202536900
    2025373,700
    2025381,900
    2025393,900
    202540200
    2025414,100
    2025422,100
    2025434,300
    2025441,100

    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, 25 and 30? (The answer is: 300). Enter the first number (e.g. '20'), the second (e.g. '25') and the third (e.g. '30'), 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, 25 and 30?

    LCM of 20, 25 and 30 is 300

    How to find the LCM of 20, 25 and 30 by prime factorization?

    Take every prime that appears in 20, 25 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 20, 25 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 25 is 100, and the LCM of 100 and 30 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, 25 and 30?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 25 and 300 ÷ 30 all come out whole. Any other common multiple of 20, 25 and 30 is a multiple of 300.

    See Also