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    LCM for 20, 36 and 48

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

    What's the Least Common Multiple (LCM) of 20, 36 and 48?

    Answer

    LCM of 20, 36 and 48 is
    720

    (Seven hundred twenty)

    720 is the smallest positive integer that 20, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 36 and 48 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor203648Highest power
    222222424
    3—32332
    55——5

    LCM = 24 × 32 × 5 = 720

    Checking the LCM of 20, 36 and 48 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, 36) = (20 × 36) ÷ 4 = 720 ÷ 4 = 180

    LCM(180, 48) = (180 × 48) ÷ 12 = 8,640 ÷ 12 = 720

    LCM(20, 36, 48) = 720

    The pairs may be taken in any order — 36 and 48 first, then 20 — and the answer is the same 720. 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, 36 and 48?. The LCM of 20, 36 and 48 is 720 — 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
    2033361,980
    2034363,060
    2035361,260
    203636180
    2036376,660
    2036383,420
    2036392,340
    203640360
    2036417,380
    2036421,260
    2036437,740
    2036441,980
    203645180
    2036464,140
    2036478,460
    203648720
    2036498,820
    203650900
    2036513,060
    2036522,340
    2036539,540
    203654540
    2036551,980
    2036562,520
    2036573,420
    2036585,220
    20365910,620
    203660180
    20366110,980
    2036625,580

    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, 36 and 48? (The answer is: 720). Enter the first number (e.g. '20'), the second (e.g. '36') and the third (e.g. '48'), 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, 36 and 48?

    LCM of 20, 36 and 48 is 720

    How to find the LCM of 20, 36 and 48 by prime factorization?

    Take every prime that appears in 20, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

    Can you get the LCM of 20, 36 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 36 is 180, and the LCM of 180 and 48 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 720 divisible by 20, 36 and 48?

    Yes, and by definition it is the smallest positive integer that is: 720 ÷ 20, 720 ÷ 36 and 720 ÷ 48 all come out whole. Any other common multiple of 20, 36 and 48 is a multiple of 720.

    See Also