traffic light at three different road crossing cheese every 48 seconds empty to 2nd and 108 seconds respectively if they change simultaneously at 7:oo a.m at what time will they change simultaneously again
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Given that traffic light at three different road crossing change after every 48 second and 108 seconds respectively.
48 = 2 × 2 × 2 × 2 × 3
108 = 2 × 2 × 3 × 3 × 3
Hence LCM of 48 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3)
= 432
That is after 432 seconds they will change simultaneously
432 seconds = 7 min 12 seconds
Thus the traffic lights change simultaneously at 7:7:12 am
48 = 2 × 2 × 2 × 2 × 3
108 = 2 × 2 × 3 × 3 × 3
Hence LCM of 48 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3)
= 432
That is after 432 seconds they will change simultaneously
432 seconds = 7 min 12 seconds
Thus the traffic lights change simultaneously at 7:7:12 am
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If the traffic lights change simultaneously at 7 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:
- 7 am + 7 minutes 12 seconds
- 07 : 07 : 12 am
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