Question

The traffic lights at three different road crossings change after every 48 seconds, 72
seconds and 108 seconds. If they start changing simultaneously at 8 a.m., after how much
time will they change again simultaneously?​

Answer 1

Answer:7.2 min

Step-by-step explanation:

find the lcm of 48 , 72 , 108

u will get 432

divide it by 60

u will get 7.2

add 8 hours + 7.2 min

u will get 8 hours 7 min approx

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