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    LCM for 8, 12 and 20

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

    What's the Least Common Multiple (LCM) of 8, 12 and 20?

    Answer

    LCM of 8, 12 and 20 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 8, 12 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 12 and 20 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

    Prime factor81220Highest power
    223222223
    3—3—3
    5——55

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 8, 12 and 20 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(8, 12) = (8 × 12) ÷ 4 = 96 ÷ 4 = 24

    LCM(24, 20) = (24 × 20) ÷ 4 = 480 ÷ 4 = 120

    LCM(8, 12, 20) = 120

    The pairs may be taken in any order — 12 and 20 first, then 8 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 12 and 20?. The LCM of 8, 12 and 20 is 120 — 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
    5812120
    681224
    7812168
    881224
    891272
    81012120
    81112264
    8121224
    81213312
    81214168
    81215120
    8121648
    81217408
    8121872
    81219456
    81220120
    81221168
    81222264
    81223552
    8122424
    81225600
    81226312
    81227216
    81228168
    81229696
    81230120
    81231744
    8123296
    81233264
    81234408

    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 8, 12 and 20? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '12') and the third (e.g. '20'), 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 8, 12 and 20?

    LCM of 8, 12 and 20 is 120

    How to find the LCM of 8, 12 and 20 by prime factorization?

    Take every prime that appears in 8, 12 and 20 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 8, 12 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 12 is 24, and the LCM of 24 and 20 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 120 divisible by 8, 12 and 20?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 12 and 120 ÷ 20 all come out whole. Any other common multiple of 8, 12 and 20 is a multiple of 120.

    See Also