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    LCM for 16, 24 and 40

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

    What's the Least Common Multiple (LCM) of 16, 24 and 40?

    Answer

    LCM of 16, 24 and 40 is
    240

    (Two hundred forty)

    240 is the smallest positive integer that 16, 24 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 24 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

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

    Prime factor162440Highest power
    224232324
    3—3—3
    5——55

    LCM = 24 × 3 × 5 = 240

    Checking the LCM of 16, 24 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(16, 24) = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

    LCM(48, 40) = (48 × 40) ÷ 8 = 1,920 ÷ 8 = 240

    LCM(16, 24, 40) = 240

    The pairs may be taken in any order — 24 and 40 first, then 16 — and the answer is the same 240. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 16, 24 and 40?. The LCM of 16, 24 and 40 is 240 — 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
    1624251,200
    162426624
    162427432
    162428336
    1624291,392
    162430240
    1624311,488
    16243296
    162433528
    162434816
    1624351,680
    162436144
    1624371,776
    162438912
    162439624
    162440240
    1624411,968
    162442336
    1624432,064
    162444528
    162445720
    1624461,104
    1624472,256
    16244848
    1624492,352
    1624501,200
    162451816
    162452624
    1624532,544
    162454432

    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 16, 24 and 40? (The answer is: 240). Enter the first number (e.g. '16'), the second (e.g. '24') 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 16, 24 and 40?

    LCM of 16, 24 and 40 is 240

    How to find the LCM of 16, 24 and 40 by prime factorization?

    Take every prime that appears in 16, 24 and 40 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

    Can you get the LCM of 16, 24 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 24 is 48, and the LCM of 48 and 40 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 240 divisible by 16, 24 and 40?

    Yes, and by definition it is the smallest positive integer that is: 240 ÷ 16, 240 ÷ 24 and 240 ÷ 40 all come out whole. Any other common multiple of 16, 24 and 40 is a multiple of 240.

    See Also