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    LCM for 20, 24 and 28

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

    What's the Least Common Multiple (LCM) of 20, 24 and 28?

    Answer

    LCM of 20, 24 and 28 is
    840

    (Eight hundred forty)

    840 is the smallest positive integer that 20, 24 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 24 and 28 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    Prime factor202428Highest power
    222232223
    3—3—3
    55——5
    7——77

    LCM = 23 × 3 × 5 × 7 = 840

    Checking the LCM of 20, 24 and 28 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, 24) = (20 × 24) ÷ 4 = 480 ÷ 4 = 120

    LCM(120, 28) = (120 × 28) ÷ 4 = 3,360 ÷ 4 = 840

    LCM(20, 24, 28) = 840

    The pairs may be taken in any order — 24 and 28 first, then 20 — and the answer is the same 840. 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, 24 and 28?. The LCM of 20, 24 and 28 is 840 — 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
    1320241,560
    142024840
    152024120
    162024240
    1720242,040
    182024360
    1920242,280
    202024120
    202124840
    2022241,320
    2023242,760
    202424120
    202425600
    2024261,560
    2024271,080
    202428840
    2024293,480
    202430120
    2024313,720
    202432480
    2024331,320
    2024342,040
    202435840
    202436360
    2024374,440
    2024382,280
    2024391,560
    202440120
    2024414,920
    202442840

    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, 24 and 28? (The answer is: 840). Enter the first number (e.g. '20'), the second (e.g. '24') and the third (e.g. '28'), 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, 24 and 28?

    LCM of 20, 24 and 28 is 840

    How to find the LCM of 20, 24 and 28 by prime factorization?

    Take every prime that appears in 20, 24 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

    Can you get the LCM of 20, 24 and 28 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 24 is 120, and the LCM of 120 and 28 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 840 divisible by 20, 24 and 28?

    Yes, and by definition it is the smallest positive integer that is: 840 ÷ 20, 840 ÷ 24 and 840 ÷ 28 all come out whole. Any other common multiple of 20, 24 and 28 is a multiple of 840.

    See Also