The circumferences of four wheels are 50 cm, 60 cm, 75 cm and 100 cm. They start moving simultaneously. What least distance should they cover so that each wheel makes a complete number of revolutions?

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Solution

Distance covered by a wheel for one complete revolution = circumference of the wheel

All the wheels will make complete numbers of revolutions when the distances covered by them is equal to their LCM.
$\begin{array}{l} 5 50, 60, 75, 100 \\ 5 10, 12, 15, 20 \\ 2 2, 12, 3, 4 \\ 2 1, 6, 3, 2 \\ 3 1, 3, 3, 1 \\ 1,1,1,1 \end{array}$
Required least distance = 5 × 5 ×2 × 2 × 3
= 25 × 4 × 3
= 300 cm = 3 m
So, each wheel will make a complete number of revolutions after travelling 3 m.

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