Three lighthouses along the Kochi coast flash every 21 seconds, 28 seconds and 36 seconds respectively. All three flash together at 7:00:00 pm.
At what time will all three next flash together?

They flash together again after LCM(21, 28, 36) seconds. $21=3\times 7,28=2^2\times$ 7 and $36=2^2\times 3^2$, so LCM = $2^2\times 3^2\times$ 7 = 252 s = 4 min 12 s, giving 7:04:12 pm. Adding the intervals (21 + 28 + 36 = 85 s) gives 7:01:25 pm; using only the longest interval gives 7:00:36 pm; doubling the LCM gives 7:08:24 pm.