SOLUTION: What is the smallest positive integer n for which 45n is a perfect cube of an integer?

Question 319260: What is the smallest positive integer n for which 45n is a perfect cube of an integer?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, factor 45n into 3*3*5*n. In order for 3*3*5*n to be a perfect cube, each prime factor must come in sets of triples. So we're missing one 3 and two 5 factors which means that n=3*5*5=75

So the answer is n=75 making the final number to be 45*75=3375

Using a calculator, we find that . We could also notice that since 3*3*3*5*5*5=3375, we can just rearrange the terms to get which would mean that (ie showing that 3375 is a perfect cube)
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