jmc

The common ratio is $$\frac{15}{\frac{3}{4}}=20$$Therefore, the $n$th term is $(20^{n-1})\left(\frac{3}{4}\right)$.

If one million (aka $10^6$) divides the $n$th term, then it must be divisible by $5^6$. This can only happen if $n-1$ is at least $6$, or $n\ge 7$.

The $7$th term is $$\left(20^6\right)\left(\frac{3}{4}\right)={\left(4\right)}^6{\left(5\right)}^6\left(\frac{3}{4}\right)=(2{)}^{10}(5{)}^6(3),$$which is divisible by $(2{)}^6(5{)}^6=10^6$, so the answer is indeed $\boxed{7}$.