Find the smallest number which on being added $23$ to it, is exactly divisible by $32,36,48,96.$

Step 1: Find L.C.M. of $32,36,48,96$:

$\begin{array}{rcl}32& =& 2\times 2\times 2\times 2\times 2\\ 36& =& 2\times 2\times 3\times 3\\ 48& =& 2\times 2\times 2\times 2\times 3\\ 96& =& 2\times 2\times 2\times 2\times 2\times 3\end{array}$

$LCM=2\times 2\times 2\times 2\times 2\times 3\times 3=288$

Step 2: Now, subtract $23$ from it:
$288-23=265$
Hence, $265$ is the required smallest number.