Q.4 Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.

The smallest 3-digit number = 100
Since LCM of 6, 8, 12
$$ \begin{array}{|l} \llap{2~~~~} 6 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array} $$ $$ \begin{array}{|l} \llap{2~~~~} 8 \\ \hline \llap{2~~~~} 4 \\ \hline \llap{2~~~~} 2 \\ \hline 1 \end{array} $$ $$ \begin{array}{|l} \llap{2~~~~} 12 \\ \hline \llap{2~~~~} 6 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array} $$ 6= 2× 3
8 = 2× 2 × 2
12 = 2 × 2 × 3
Then LCM = 2 × 2 × 3 × 2 = 24
Now we need to find the smallest 3-digit multiple of 24
\(\therefore \) 24 × 4 = 96 and 24 × 5 = 120
Hence, 120 is the smallest 3-digit number which is exactly divisible by 6, 8 and 12