Question

a traffic lights of three different roads full stop Crossings change after every 48 second 72 second and 108 seconds respectively if they change simultaneously at 7:00 a.m. at what time will they change simultaneously again​

Answer 1

Answer:

next time 7 hour 7 minute 12 seconds(am)

Will they changed

Step-by-step explanation:

lcm of 48,72,108

is 432 in seconds

432 sec=7 minutes 12 seconds

Answer 2

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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

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