  Let $p$ be a large prime number, $K,L,M,\lambda$ be integers with $1\le M\le
p$ and ${\color{red}\gcd}(\lambda,p)=1.$ The aim of our paper is to obtain
sharp upper bound estimates for the number $I_2(M; K,L)$ of solutions of the
congruence $$ xy\equiv\lambda \pmod p, \qquad K+1\le x\le K+M,\quad L+1\le y\le
L+M $$ and for the number $I_3(M;L)$ of solutions of the congruence
$$xyz\equiv\lambda\pmod p, \quad L+1\le x,y,z\le L+M. $$ We obtain a bound for
$I_2(M;K,L),$ which improves several recent results of Chan and Shparlinski.
For instance, we prove that if $M<p^{1/4},$ then $I_2(M;K,L)\le M^{o(1)}.$ For
$I_3(M;L)$ we prove that if $M<p^{1/8}$ then $I_3(M;L)\le M^{o(1)}.$ Our
results have applications to some other problems as well. For instance, it
follows that if $\mathcal{I}_1, \mathcal{I}_2, \mathcal{I}_3$ are intervals in
$\F^*_p$ of length $|\mathcal{I}_i|< p^{1/8},$ then $$ |\mathcal{I}_1\cdot
\mathcal{I}_2\cdot \mathcal{I}_3|= (|\mathcal{I}_1|\cdot |\mathcal{I}_2|\cdot
|\mathcal{I}_3|)^{1-o(1)}. $$
