Find the smallest 6-digit number which is exactly divisible by 63.

The smallest 6-digit number = 1,00,000.

To find the smallest 6-digit number exactly divisible by 63, we divide 1,00,000 by 63 and add the difference between the divisor and remainder to 1,00,000.

$\begin{array}{l} \phantom{x^2 }{\quad 1587} \ 63\overline{\smash{\big)}100000} \ \phantom{x}\phantom{)}\underline{-63} \ \phantom{x^2+} 370 \ \phantom{{x}+}\underline{-315} \ \phantom{{x^2 }2x + } 550 \ \phantom{{x}+ 11}\underline{-504} \ \phantom{{x^2 + 3x))}} 460 \ \phantom{{x} + 1x)}\underline{-441} \ \phantom{{x^2 + 3x)44}} 19\ \end{array}$

Required number to be added = 63 − 19 = 44

Number = 1,00,000 + 44 = 1,00,044.

Hence, the smallest 6-digit number exactly divisible by 63 = 1,00,044.