Four runners started running simultaneously from a point on a circular track. They took 280 seconds, 350 seconds, 420 seconds and 560 seconds, respectively, to complete one round. After how much time (in seconds) do they meet at the starting point for the first time?

Correct option is D

Given:

Time taken by four runners to complete one round:

280 sec, 350 sec, 420 sec, 560 sec

Solution:

Prime factorization:

​$$280 = 2^3 \times 5 \times 7 \\ \ \\ 350 = 2 \times 5^2 \times 7 \\ \ \\ 420 = 2^2 \times 3 \times 5 \times 7 \\ \ \\ 560 = 2^4 \times 5 \times 7$$​

LCM = $$2^4 \times 3 \times 5^2 \times 7$$ = 8400 sec