Traffic lights at three different road crossing changes after 48 sec, 72 sec and 108 sec respectively. At which time Will they change together again if they change simultaneously at 7 A.M.?
Answers
Answered by
1
Answer:
7:07:12 AM
Step-by-step explanation:
Calculate the LCM of these three, i.e.,
432.
Which means the signals will change again simultaneously after 432 seconds. ( 7mins 12 seconds)
Answered by
0
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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