Math, asked by amareshsinghpatel, 1 year ago

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 vasugupta2384
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 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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