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    LCM for 24, 32 and 40

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

    What's the Least Common Multiple (LCM) of 24, 32 and 40?

    Answer

    LCM of 24, 32 and 40 is
    480

    (Four hundred eighty)

    480 is the smallest positive integer that 24, 32 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 24, 32 and 40 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    Prime factor243240Highest power
    223252325
    33——3
    5——55

    LCM = 25 × 3 × 5 = 480

    Checking the LCM of 24, 32 and 40 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(24, 32) = (24 × 32) ÷ 8 = 768 ÷ 8 = 96

    LCM(96, 40) = (96 × 40) ÷ 8 = 3,840 ÷ 8 = 480

    LCM(24, 32, 40) = 480

    The pairs may be taken in any order — 32 and 40 first, then 24 — and the answer is the same 480. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 24, 32 and 40?. The LCM of 24, 32 and 40 is 480 — 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
    2425322,400
    2426321,248
    242732864
    242832672
    2429322,784
    243032480
    2431322,976
    24323296
    2432331,056
    2432341,632
    2432353,360
    243236288
    2432373,552
    2432381,824
    2432391,248
    243240480
    2432413,936
    243242672
    2432434,128
    2432441,056
    2432451,440
    2432462,208
    2432474,512
    24324896
    2432494,704
    2432502,400
    2432511,632
    2432521,248
    2432535,088
    243254864

    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 24, 32 and 40? (The answer is: 480). Enter the first number (e.g. '24'), the second (e.g. '32') and the third (e.g. '40'), 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 24, 32 and 40?

    LCM of 24, 32 and 40 is 480

    How to find the LCM of 24, 32 and 40 by prime factorization?

    Take every prime that appears in 24, 32 and 40 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 × 5 = 480.

    Can you get the LCM of 24, 32 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 24 and 32 is 96, and the LCM of 96 and 40 is 480 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 480 divisible by 24, 32 and 40?

    Yes, and by definition it is the smallest positive integer that is: 480 ÷ 24, 480 ÷ 32 and 480 ÷ 40 all come out whole. Any other common multiple of 24, 32 and 40 is a multiple of 480.

    See Also