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Math Help - Finding the smallest positive integral value of n

  1. #1
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    Finding the smallest positive integral value of n

    "Find the smallest positive integral value of n for which the following product is an integer.

    (1\frac{1}{36}) (1\frac{1}{37}) ... (1\frac{1}{n})

    Justify your answer."

    If anybody could give me a hint on how to find this I would appreciate it. Thanks!
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  2. #2
    MHF Contributor red_dog's Avatar
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    The product is equal to

    \frac{37}{36}\cdot\frac{38}{37}\cdot\ldots\cdot\fr  ac{n}{n-1}\cdot\frac{n+1}{n}=\frac{n+1}{36}

    The smallest multiple of 36, greater than 36, is 72.

    Then, n+1=72\Rightarrow n=71
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