Find the smallest value of k such that 525k is a perfect cub
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If you decompose in prime factors, you get 175=52⋅7 so the smallest perfect cube is the number that we must multiply by 5 and by 7 so to create the smallest perfect cube, i.e. 53⋅73 .
This number is k=5⋅72=245 .
In fact 245×175=42875=353
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