Question

A circular field has a circumference of $360$ km. Three cyclists start together and can cycle 48,60 and 72 km a day, round the field. When will they meet again?

Answer 1

So time taken for cyclist1 $=\frac{360}{48}=7.5$ days

time $t$ taken for cyclist2 $=\frac{360}{60}=6$ days

time taken for cyclist3 $=\frac{360}{72}=5$ days

Here we can see $7.5,6,5$ is in LCM so we have to get LCM of $7.5,6,5$ i.e $30$

so they will meet after 30 days.

in 30 days first cyclist will travel $= \dfrac{30}{7.5}= 4 rounds

in 30 days 2nd cyclist will travel $=\frac{30}{6}=5$ rounds

in 30 days third cyclist will travel $=\frac{30}{5}=6$ rounds

so after $30$ days all the three cyclists will meet at start point.