Find a natural number n, in canonical form, such than n/2=a^2 , n/3=b^3 , n/5= c^5 for some a,b,c (natural numbers)
$\displaystyle n$ is divisible by 2, 3, and 5, so try $\displaystyle n=2^r3^s5^t$. Then $\displaystyle r$ must be divisible by 3 and 5, $\displaystyle s$ must be divisible by 2 and 5, and $\displaystyle t$ must be divisible by 2 and 3. Hence one possible value for $\displaystyle n$ is $\displaystyle 2^{15}3^{10}5^{6}$.