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 18, 20 and 36

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

    What's the Least Common Multiple (LCM) of 18, 20 and 36?

    Answer

    LCM of 18, 20 and 36 is
    180

    (One hundred eighty)

    180 is the smallest positive integer that 18, 20 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 20 and 36 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor182036Highest power
    22222222
    332—3232
    5—5—5

    LCM = 22 × 32 × 5 = 180

    Checking the LCM of 18, 20 and 36 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(18, 20) = (18 × 20) ÷ 2 = 360 ÷ 2 = 180

    LCM(180, 36) = (180 × 36) ÷ 36 = 6,480 ÷ 36 = 180

    LCM(18, 20, 36) = 180

    The pairs may be taken in any order — 20 and 36 first, then 18 — and the answer is the same 180. 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/18--20--36Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/18--20--36">What is the LCM of 18, 20 and 36? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 18, 20 and 36?. The LCM of 18, 20 and 36 is 180 — 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/18--20--36/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    1820211,260
    1820221,980
    1820234,140
    182024360
    182025900
    1820262,340
    182027540
    1820281,260
    1820295,220
    182030180
    1820315,580
    1820321,440
    1820331,980
    1820343,060
    1820351,260
    182036180
    1820376,660
    1820383,420
    1820392,340
    182040360
    1820417,380
    1820421,260
    1820437,740
    1820441,980
    182045180
    1820464,140
    1820478,460
    182048720
    1820498,820
    182050900

    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 18, 20 and 36? (The answer is: 180). Enter the first number (e.g. '18'), the second (e.g. '20') and the third (e.g. '36'), 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 18, 20 and 36?

    LCM of 18, 20 and 36 is 180

    How to find the LCM of 18, 20 and 36 by prime factorization?

    Take every prime that appears in 18, 20 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

    Can you get the LCM of 18, 20 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 20 is 180, and the LCM of 180 and 36 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 180 divisible by 18, 20 and 36?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 18, 180 ÷ 20 and 180 ÷ 36 all come out whole. Any other common multiple of 18, 20 and 36 is a multiple of 180.

    See Also