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25 February, 07:40

How do you find the smallest positive integer k such that 1350k is a perfect cube?

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  1. 25 February, 07:41
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    A cube is x*x*x

    prime factor 1350

    1350*k

    5*270*k

    5*3*90*k

    5*3*3*30*k

    5*3*3*3*10*k

    5*3*3*3*2*5*k

    what value does k have to be to have three of each prime factor?

    k = 5*2*2 = 20

    Then 1350*20 = 27,000 = (5*3*2) ^3
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