Q.9 Find the smallest 4-digit number which is divisible by 18, 24 and 32.

The smallest 4-digit number = 1000.
$$ \begin{array}{|l} \llap{2~~~~} 18, 24, 32 \\ \hline \llap{2~~~~} 9, 12, 16 \\ \hline \llap{2~~~~} 9, 6, 8 \\ \hline \llap{3~~~~} 9, 3, 4 \\ \hline 3, 1, 4 \end{array} $$ LCM = 2 x 2 x 2 x 3 x 3 x 4 = 288
Here, we need to find the smallest 4-digit multiple of 288
\(\therefore \) 288 × 3 = 864 and 288 × 4 = 1152
Hence, 1152 is the smallest 4-digit number which is divisible by 18, 24 and 32