In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms…

Minimum number of rooms required means there should be maximum number of teachers in a room. We have to find HCF of $\displaystyle 48$, $\displaystyle 80$ and 144. \[48=2^{4} \times 3 \] \(\displaystyle 80=2^{4} \times 5\) \(\displaystyle 144=2^{4} \times 3^{2}\) \(\displaystyle \operatorname{HCF}(48,80,144)=2^{4}=16\) Therefore, total number of rooms required \(\displaystyle =\frac{48}{16}+\frac{80}{16}+\frac{144}{16}=17\)