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    LCM for 10, 25 and 40

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

    What's the Least Common Multiple (LCM) of 10, 25 and 40?

    Answer

    LCM of 10, 25 and 40 is
    200

    (Two hundred)

    200 is the smallest positive integer that 10, 25 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 25 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 25: 5 × 5 (exponent form: 52)

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

    Prime factor102540Highest power
    22—2323
    5552552

    LCM = 23 × 52 = 200

    Checking the LCM of 10, 25 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(10, 25) = (10 × 25) ÷ 5 = 250 ÷ 5 = 50

    LCM(50, 40) = (50 × 40) ÷ 10 = 2,000 ÷ 10 = 200

    LCM(10, 25, 40) = 200

    The pairs may be taken in any order — 25 and 40 first, then 10 — and the answer is the same 200. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 25 and 40?. The LCM of 10, 25 and 40 is 200 — 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
    10252550
    102526650
    1025271,350
    102528700
    1025291,450
    102530150
    1025311,550
    102532800
    1025331,650
    102534850
    102535350
    102536900
    1025371,850
    102538950
    1025391,950
    102540200
    1025412,050
    1025421,050
    1025432,150
    1025441,100
    102545450
    1025461,150
    1025472,350
    1025481,200
    1025492,450
    10255050
    1025512,550
    1025521,300
    1025532,650
    1025541,350

    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 10, 25 and 40? (The answer is: 200). Enter the first number (e.g. '10'), the second (e.g. '25') 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 10, 25 and 40?

    LCM of 10, 25 and 40 is 200

    How to find the LCM of 10, 25 and 40 by prime factorization?

    Take every prime that appears in 10, 25 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 5² = 200.

    Can you get the LCM of 10, 25 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 25 is 50, and the LCM of 50 and 40 is 200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 200 divisible by 10, 25 and 40?

    Yes, and by definition it is the smallest positive integer that is: 200 ÷ 10, 200 ÷ 25 and 200 ÷ 40 all come out whole. Any other common multiple of 10, 25 and 40 is a multiple of 200.

    See Also