Question

Jackson and Levi were jogging on a circular track. In a given duration, Jackson covers one round of the circular track in 3 minutes while Levi covers one round in 2 minutes. On one evening, they started together from the same starting point and in same direction. Find the least number of minutes after which they again meet at the starting point.

• A. $2$
• B. $3$
• C. $6$
• D. $12$

Answer 1

The correct option is C $6$

Jackson and Levi return to the starting point after $3\text{min}$ and $2\text{min}$ respectively.

$\therefore$ Total time each friend takes is a common multiple of $2$ and $3.$

Few multiples of $2$ and $3$ are:
$2\times 1=2$
$2\times 2=4$
$2\times 3=6$
$2\times 4=8$

$3\times 1=3$
$3\times 2=6$
$3\times 3=9$
$2\times 4=12$

The least number of minutes is given by the common multiple of $2$ and $3,$ i.e., $6\text{min}.$

After $6\text{min}$, they again meet at the starting point.
In these 6 minutes, Jaqckson covered 2 rounds and Levi covered 3 rounds.