smc

Since the harmonic mean is $2$ times their product divided by their sum, we get the equation $\frac{2\times 1\times 2016}{1+2016}$ which is then $\frac{4032}{2017}$ which is finally closest to $\boxed{\text{(A)}2}$. You can also think of $\frac{2\times 1\times 2016}{1+2016}$ as $2\times \frac{2016}{2017}$ which it should be obvious that our number is most closest to 2 ($\lceil \frac{2016}{2017}\rceil =1$), our answer here is $\boxed{2}$