In a teachers' workshop, the number of teachers teaching French, Hindi and English are $\displaystyle 48$, $\displaystyle 80$ and $\displaystyle 144$ respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject.

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 \(\displaystyle =\frac{48}{16}+\frac{80}{16}+\frac{144}{16}=17\)