There is a circular path around a sports field. Sonia takes \(18\) minutes to drive one round of the field, while Ravi takes \(12\) minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Question

Express each number as a product of its prime factors:

\(140\)
\(156\)
\(3825\)
\(5005\)
\(7429\)

Answer 1

Ravi completes one round of the circular path in less time than Sonia. Since they are moving in the same direction, they will meet again when Ravi has completed \(1\) round \(5\) more than Sonia. The time taken for them to meet again at the starting point is the Least Common Multiple (LCM) of the time each takes to complete one round, which are \(18\) minutes for Sonia and \(12\) minutes for Ravi.
\(18 = 2 \times 3 \times 3\)
And, \(12 = 2 \times 2 \times 3\)
LCM of \(12\) and \(18 = 2 \times 2 \times 3 \times 3 = 36\)

Consequently, Ravi and Sonia will reunite at the starting point after \(36\) minutes.

Solution and Explanation

Top Questions on The Fundamental Theorem of Arithmetic

Questions Asked in CBSE Class X exam