How to find square and cubes

Question

I want to find the smallest positive integer A in which $$10A$$ is a perfect square and $$6A$$ is a perfect cube

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Thanks for the hint, I can see now I just needed $$2^5,3^2 , 5^3$$

Answer 1

Hint: if you factor a square into prime factors, say $n^2=p_1^{a_1}p_2^{a_2}\dots$ where the $p_i$ are primes, all the $a_i$ will be even. Similarly for a cube, the $a_i$ will be multiples of $3$. Here your primes are only $2,3,5$