Question

two light houses flash light together at 7 p.m. if one lighthouse flashes every 21 seconds and the other flashes every 35 seconds, when will the two lighthouses flash together next ?

Answer 1

To find the maximum time, we have to find the LCM of 21,35
by prime factorisation,
21=3×7
35=7×5
LCM=3×7×5
=105 minutes
=1 hour 45 minutes
therefore,at 8:45pm,they will flash together.

Answer 2

The two light houses will flash together after (LCM of 21 and 35) seconds I.e.105 seconds later which means 105/60 mins later I.e. at 7:01:45 PM. The 21 seconds flash light would have flashed 105/21=5 times by then and the 35 seconds one would have flashed 3 times by then.