Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference ownwards. Find when they will again come together in the same position.

First wheel makes 60 revolutions in 1 minute

$$\Rightarrow$$ It makes 60 revolutions in 60 seconds

$$\Rightarrow$$ It makes 1 revolution in 1 second.

This implies, after every 1 second the certain point at which the wheel started its revolution reaches its initial position.

Similarly, Second wheel and Third wheel makes 36 and 24 revolutions in 1 minute respectively.

$$\Rightarrow$$ Second and Third wheel makes 1 revolution in $$\frac{5}{3} and \frac{5}{2}$$ seconds respectively.

So for all the multiples of $$\frac{5}{3} and \frac{5}{2}$$ seconds the certain point of second wheel and third wheel reaches its initial position respectively.

After LCM {1, $$\frac{5}{3}, \frac{5}{2}$$} seconds all the three wheels will come together in the same position.

LCM of fractions = LCM of numerators/ HCF of denominators 

$$\Rightarrow$$ LCM {1,$$\frac{5}{3}, \frac{5}{2}$$} = LCM {1,5,5}$$\div$$HCF {1,3,2} = 5$$\div$$1 = 5.

Hence, after 5 seconds all the wheels will come again together in the same position.