Revolutions of three wheels

Time taken for 1 revolution by each wheel:

• First wheel: 60 rev/min = 1 rev/sec $\implies 1$ second.
• Second wheel: 36 rev/min = $\frac{36}{60} = \frac{3}{5}$ rev/sec $\implies \frac{5}{3}$ seconds.
• Third wheel: 24 rev/min = $\frac{24}{60} = \frac{2}{5}$ rev/sec $\implies \frac{5}{2}$ seconds.

They will come together after $\text{LCM}\left(1, \frac{5}{3}, \frac{5}{2}\right)$ seconds. $\text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{\text{LCM}(1, 5, 5)}{\text{HCF}(1, 3, 2)} = \frac{5}{1} = 5\text{ seconds.}$