At a school sports meet, 60 students enter for kho-kho, 84 for kabaddi and 108 for the relay. They are to be seated in rooms with the same number of students in each room, and every room holding entrants of only one event. What is the minimum number of rooms required?

**Theorem**: A rational number $\frac{p}{q}$ (in lowest terms) has a terminating decimal expansion if and only if $q$ has the form **2ᵐ × 5ⁿ** (m, n ≥ 0).

**Examples**:
- $\frac{3}{8}:q=8=2^3$ → terminates$.(\frac{3}{8}=\mathrm{0.375.})-\frac{7}{40}:q=40=2^3\times 5$ → terminates$.(\frac{7}{40}=\mathrm{0.175.})-\frac{1}{3}:q=3$ → does NOT terminate$.(\frac{1}{3}=0.333$… recurring.)
- $\frac{4}{15}:q=15=3\times 5$ → does NOT terminate (because of the 3).

**Why**: any decimal expansion is a fraction with denominator 10ⁿ = 2ⁿ × 5ⁿ. To convert $\frac{p}{q}$ to decimal form, you need $q$ to ONLY have 2s and 5s as primes — otherwise you can't multiply numerator/denominator into a power of 10.