the traffic lights at three different road Crossings change after every 48 seconds 72 seconds and 108 second respectively. if they change simultaneously at 7:00 a.m. at what time will they change simultaneously again
Answers
Answer:
7:07:12 a.m
Step-by-step explanation:
Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.
So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds
48 = 2 × 2 × 2 × 2 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
Hence LCM of 48, 72 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3) = 432
So after 432 seconds they will change simultaneously
We know that 60 seconds = 1 minute
so on dividing 432 / 60 we get 7 as quotient and 12 as reminder
Hence, 432 seconds = 7 min 12 seconds
Therefore the time is = 7 a.m. + 7 minutes 12 seconds
Hence the lights change simultaneously at = 7:07:12 a.m
If the traffic lights change simultaneously at 8 a.m, then they will change simultaneously again after the LCM of the duration i.e. 48 s, 72 s and 108 s.
LCM of these durations by prime factorisation,,
- 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3
- 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
- 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³
LCM of 48, 72 and 108 is 2⁴ × 3³ = 432 seconds.
Hence, They will change after 432 seconds i.e. 7 minutes 12 seconds.
The traffic lights will change after:
- 8 am + 7 minutes 12 seconds
- 08 : 07 : 12 am