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    LCM for 8, 20 and 24

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

    What's the Least Common Multiple (LCM) of 8, 20 and 24?

    Answer

    LCM of 8, 20 and 24 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 8, 20 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 20 and 24 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    Prime factor82024Highest power
    223222323
    3——33
    5—5—5

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 8, 20 and 24 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, 20) = (8 × 20) ÷ 4 = 160 ÷ 4 = 40

    LCM(40, 24) = (40 × 24) ÷ 8 = 960 ÷ 8 = 120

    LCM(8, 20, 24) = 120

    The pairs may be taken in any order — 20 and 24 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, 20 and 24?. The LCM of 8, 20 and 24 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
    8920360
    8102040
    81120440
    81220120
    81320520
    81420280
    81520120
    8162080
    81720680
    81820360
    81920760
    8202040
    82021840
    82022440
    82023920
    82024120
    82025200
    82026520
    820271,080
    82028280
    820291,160
    82030120
    820311,240
    82032160
    820331,320
    82034680
    82035280
    82036360
    820371,480
    82038760

    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, 20 and 24? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '20') and the third (e.g. '24'), 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, 20 and 24?

    LCM of 8, 20 and 24 is 120

    How to find the LCM of 8, 20 and 24 by prime factorization?

    Take every prime that appears in 8, 20 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 8, 20 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 20 is 40, and the LCM of 40 and 24 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, 20 and 24?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 20 and 120 ÷ 24 all come out whole. Any other common multiple of 8, 20 and 24 is a multiple of 120.

    See Also