Question

Traffic lights at three different points are changing respectively at 24, 48 and 72 seconds. if all the three are changed together at 9:10:24 hours, then when will the next change take place together

Answer 1

L.C.M of 24,48,72 =144
They will change again together after 144 sec i.e after 2 minutes and 24 seconds.

Hence ,they will change together again at 9:12:48

Answer 2

Lights will again change together at 9:12:48

1) First light changes after 24 seconds.

Second light changes after 48 seconds.

Third light changes after 72 seconds.

2) All three of these lights would change together at a common multiple of 24,28,72.

3) Least common multiple of 24,48,72 is 144.

4) Hence, lights will change color together after 144 seconds or 2 minutes 24 seconds.

5) Time given is 9:10:24, then lights will again change together at 9:12:48