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    LCM for 40, 50 and 80

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

    What's the Least Common Multiple (LCM) of 40, 50 and 80?

    Answer

    LCM of 40, 50 and 80 is
    400

    (Four hundred)

    400 is the smallest positive integer that 40, 50 and 80 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 40, 50 and 80 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

    All Prime Factors of 80: 2 × 2 × 2 × 2 × 5 (exponent form: 24 × 5)

    Prime factor405080Highest power
    22322424
    5552552

    LCM = 24 × 52 = 400

    Checking the LCM of 40, 50 and 80 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(40, 50) = (40 × 50) ÷ 10 = 2,000 ÷ 10 = 200

    LCM(200, 80) = (200 × 80) ÷ 40 = 16,000 ÷ 40 = 400

    LCM(40, 50, 80) = 400

    The pairs may be taken in any order — 50 and 80 first, then 40 — and the answer is the same 400. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 40, 50 and 80?. The LCM of 40, 50 and 80 is 400 — 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
    4050652,600
    4050666,600
    40506713,400
    4050683,400
    40506913,800
    4050701,400
    40507114,200
    4050721,800
    40507314,600
    4050747,400
    405075600
    4050763,800
    40507715,400
    4050787,800
    40507915,800
    405080400
    40508116,200
    4050828,200
    40508316,600
    4050844,200
    4050853,400
    4050868,600
    40508717,400
    4050882,200
    40508917,800
    4050901,800
    40509118,200
    4050924,600
    40509318,600
    4050949,400

    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 40, 50 and 80? (The answer is: 400). Enter the first number (e.g. '40'), the second (e.g. '50') and the third (e.g. '80'), 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 40, 50 and 80?

    LCM of 40, 50 and 80 is 400

    How to find the LCM of 40, 50 and 80 by prime factorization?

    Take every prime that appears in 40, 50 and 80 to the highest power it reaches in any one of them and multiply: 2⁴ × 5² = 400.

    Can you get the LCM of 40, 50 and 80 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 40 and 50 is 200, and the LCM of 200 and 80 is 400 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 400 divisible by 40, 50 and 80?

    Yes, and by definition it is the smallest positive integer that is: 400 ÷ 40, 400 ÷ 50 and 400 ÷ 80 all come out whole. Any other common multiple of 40, 50 and 80 is a multiple of 400.

    See Also