Problem #PRU-100294

Problem

Denote by $\overline{ab}=10a+b$ the two-digit number whose first and second digits are $a$ and $b$ respectively. Do there exist two $2$-digit numbers $\overline{ab}$ and $\overline{cd}$ such that $\overline{ab}\times \overline{cd}=\overline{abcd}$? (Here $\overline{abcd}$ is a four-digit number with digits $a$, $b$, $c$ and $d$, i.e. $\overline{abcd}=1000a+100b+10c+d$.)