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    LCM for 24, 36 and 40

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

    What's the Least Common Multiple (LCM) of 24, 36 and 40?

    Answer

    LCM of 24, 36 and 40 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 24, 36 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 24, 36 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

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

    Prime factor243640Highest power
    223222323
    3332—32
    5——55

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 24, 36 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, 36) = (24 × 36) ÷ 12 = 864 ÷ 12 = 72

    LCM(72, 40) = (72 × 40) ÷ 8 = 2,880 ÷ 8 = 360

    LCM(24, 36, 40) = 360

    The pairs may be taken in any order — 36 and 40 first, then 24 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 24, 36 and 40?. The LCM of 24, 36 and 40 is 360 — 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
    2425361,800
    242636936
    242736216
    242836504
    2429362,088
    243036360
    2431362,232
    243236288
    243336792
    2434361,224
    2435362,520
    24363672
    2436372,664
    2436381,368
    243639936
    243640360
    2436412,952
    243642504
    2436433,096
    243644792
    243645360
    2436461,656
    2436473,384
    243648144
    2436493,528
    2436501,800
    2436511,224
    243652936
    2436533,816
    243654216

    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, 36 and 40? (The answer is: 360). Enter the first number (e.g. '24'), the second (e.g. '36') 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, 36 and 40?

    LCM of 24, 36 and 40 is 360

    How to find the LCM of 24, 36 and 40 by prime factorization?

    Take every prime that appears in 24, 36 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 24, 36 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 24 and 36 is 72, and the LCM of 72 and 40 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 24, 36 and 40?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 24, 360 ÷ 36 and 360 ÷ 40 all come out whole. Any other common multiple of 24, 36 and 40 is a multiple of 360.

    See Also