**Q) **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 together next?

**Ans: **

The three traffic light will change together again when the time gap is perfect multiple of each light’s interval.

Therefore, we will take LCM of all three time intervals

LCM of 48 , 72, 108 = 2^{4} x 3^{3} = 16 x 9 x 3 = 576 x 3 = 432 seconds = 7 minutes 12 seconds

*[48 = 2 ^{4 }x 3, 72 = 2^{3 }x 3^{2}, 108 = 2^{2 }x 3^{3 }]*

New time of ringing together = 7:00 am + 7 mins 12 seconds = 7:07:12 am

**Therefore, three bells will ring together at 7:07:12 a.m. **