Question

Anil and Sunil are practicing for sports day. Anil can run for $20$ minutes before taking a break, and Sunil can run for $15$ minutes before taking a break. After how many minutes will they take a break together?

Answer 1

We have given

Anil can run without break for $\text{20 minutes}$

Sunil can run without break for $\text{15 minutes}$

Both Anil and Sunil take a break together again is the L.C.M. of $20and15$

Finding the L.C.M. by prime factorization method

$$\begin{gathered} \text{Multiple of 20 are 20, 40, 60, 80, 100, 120....} \\ \text{Multiple of 15 are 15, 30, 45, 60, 75, 90, 105, 120....} \\ \text{least common multiple of 20 and 15 is 60} \\ \text{lcm(20, 15)= 60} \end{gathered}$$

Hence, both Anil and Sunil together take a break after $\text{60 minutes or 1 hour}$.