Math, asked by Irony14, 1 year ago

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

Answers

Answered by chandresh126
2
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
Answered by BrainlyPARCHO
0

 \large \green{  \fcolorbox{gray}{black}{ ☑ \:  \textbf{Verified \: answer}}}

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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