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., what time will they charge simultaneously again?
Answers
Answer:
Answer:7:00:48
Answer:7:00:487:01:12
Answer:7:00:487:01:127:01:48
Answer:7:00:487:01:127:01:48on this time the traffic lite is Blum at the time if 7 am .in the morning time for your information.
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
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