Math, asked by Sheilas, 1 year ago

The traffic light at three different road crossing change after every 48 second ,72 second and 108 second respectively. If they all change simultaneously at 8 am,then at what time will they again change simultaneously give in detail

Answers

Answered by misha2054
0
Sorry I don't know this answer
Answered by BrainlyPARCHO
0

 \large \green{  \fcolorbox{grey}{white}{ ☑ \:  \textbf{Verified \: answer}}}

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

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