Find the smallest five-digit number which is exactly divisible by 254

The smallest 5-digit number = 10000.

To find the smallest 5-digit number exactly divisible by 254, we divide 10000 by 254 and add the difference between the divisor and remainder to 10000.

$\begin{array}{l} \phantom{x^2()}{\quad 39} \ 254\overline{\smash{\big)}10000} \ \phantom{x^+(}\phantom{}\underline{-762} \ \phantom{{x^2 }(())} 2380 \ \phantom{{x}+}\underline{-2286} \ \phantom{{x^2 +++}} 94 \ \end{array}$

The remainder when 10000 is divided by 254 is 94.

Required number to be added = 254 - 94 = 160.

Number = 10000 + 160 = 10160.

Hence, the smallest five-digit number which is exactly divisible by 254 is 10160.