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  1. #1
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    The numbers 168 and 324, written as the products of their prime factors, are 168=2(cube)󫢯, 324=2(sq)3(4)

    Find the smallest positive integer value of n for which 168n is a multiple of 324.



    Please help

    (Sorry, I can't put type the square or cube on top of the numbers. )
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  2. #2
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    Quote Originally Posted by kismyjacq View Post
    The numbers 168 and 324, written as the products of their prime factors, are 168=2(cube)󫢯, 324=2(sq)3(4)

    Find the smallest positive integer value of n for which 168n is a multiple of 324.



    Please help

    (Sorry, I can't put type the square or cube on top of the numbers. )
    168 = 2^2 \times 3 \times 2 \times 7.

    324 = 2^2 \times 3 \times 3^3.

    Therefore 168 \times 3^3 = 324 \times 2 \times 7.

    Since 3^3 has no common factor with 2 \times 7 it follows that n = 3^3 = 27.
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