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Math Help - Positive integer and factor

  1. #1
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    Positive integer and factor

    Im stuck on this question:

    What is the smallest positive integer that is divisible by the factor 2,3 and 5 and which is also square and a cube. Prove that this is the smallest such integer.

    how would i start this?

    thanks
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  2. #2
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    Re: Positive integer and factor

    In the prime factorization of a perfect square, the exponent of each factor must divide 2. Similarly, for a perfect cube, the exponent of each factor must divide 3. So, your answer is going to be  (2\cdot3\cdot5)^6.

    This is how I would start the process of answering the problem. The language of the formal proof is the next step.
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  3. #3
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    Re: Positive integer and factor

    Quote Originally Posted by DiamondVH123 View Post
    What is the smallest positive integer that is divisible by the factor 2,3 and 5 and which is also square and a cube. Prove that this is the smallest such integer.

    Is 2^6 the smallest multiple of two that is both a square and a a cube?
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  4. #4
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    Re: Positive integer and factor

    Thanks i know how to answer it now
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