Jyoti, Kavya, Shivam and Manish start walking from the same point in the same direction around a rectangular track and each one of them completes one round in 180 seconds, 270 seconds, 360 seconds and 240 seconds respectively. After how much time will they all meet again at one point ?

Correct option is D

Given:

Jyoti's time for one round = 180 seconds.

Kavya's time for one round = 270 seconds.

Shivam's time for one round = 360 seconds.

Manish's time for one round = 240 seconds.

Solution:
Prime factorizations:

180 =$$2^2 \times 3^2 \times 5$$​​

270$$= 2 \times 3^3 \times 5$$​​

360 =$$2^3 \times 3^2 \times 5$$​​

240 = $$2^4 \times 3 \times 5$$​​

So, the LCM is:
LCM = $$2^4 \times 3^3 \times 5 = 16 \times 27 \times 5 = 2,160 \text{ seconds}$$​​

​$$2,160 \text{ seconds} = \frac{2,160}{60} = 36 \text{ minutes}.$$​​

Thus, they will all meet again after 36 minutes.