Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m. at what time will they change simultaneously again?

Answer 1

L.C.M. of 48, 72, 108 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432 sec.

After 432 seconds, the lights change simultaneously.

432 second = 7 minutes 12 seconds

Therefore the time = 7 a.m. + 7 minutes 12 seconds

= 7 : 07 : 12 a.m.

Answer 2

L.C.M of 48,72,108 can be taken to find the intervals of change =432 sec

After 432 sec  = 432÷(60×60)      =432÷3600        =0.12 hrs

Hence, next simultaneous change will take place at = 8.00 am +0.12  =8.12 am