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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 required if in each room the same number of teachers are seated and all of them are of the same subject.
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Sol. Minimum number of rooms required means there should be maximum number of teachers in a room. We have to find HCF of $48, 80$ and $144$.
$48 = 2^4 \times 3$
$80 = 2^4 \times 5$
$144 = 2^4 \times 3^2$
HCF $(48, 80, 144) = 2^4 = 16$
Therefore, total number of rooms required = $\frac{48}{16} + \frac{80}{16} + \frac{144}{16} = 17$
$48 = 2^4 \times 3$
$80 = 2^4 \times 5$
$144 = 2^4 \times 3^2$
HCF $(48, 80, 144) = 2^4 = 16$
Therefore, total number of rooms required = $\frac{48}{16} + \frac{80}{16} + \frac{144}{16} = 17$