Phi

$\phi(x)=x(1-\frac{1}{p})(1-\frac{1}{q})=p^2q^2*\frac{p-1}{p}*\frac{q-1}{q}=pq(p-1)(q-1)$

$\phi(x)=840=2^3*3*5*7$ Suppose $p<q$ . So $p$ , $p-1$ , $q-1$ are smaller than $q$ . $\phi(x)$ 's biggest prime divisor is $7$ , so $q=7$ .

$p(p-1)=\frac{\phi(x)}{q(q-1)}=\frac{2^3*3*5*7}{7*6}=2^2*5$ .

In the left side the biggest prime divisor is $p$ , in the right side is $5$ , so $p=5$ . The only solution is:

$x=p^2q^2=5^2*7^2=25*49=\boxed{1225}$