The traffic lights at three different road crossings change after every 72 seconds, 108 seconds and 132 seconds respectively. If they change simultaneously at 7.am, at what time will they change again simultaneously.
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.
Answer:
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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
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: