Question

the traffic lights at three different road crossings change after every 48 seconds 72 seconds and108 secs .if they all change simultaneously at 8hours then, at what time will be again change simultaneously ​

Answer 1

Answer:

Firstly we will take the LCM (least common multiple) which is equal to 442.

Hence they will change simultaneously after 442 seconds.

=442/60= 7.31 minutes (approx.)

Hence they will change again at 8:00 hours +7.31 minutes = 8:7.31 hours.

Thank you

Answer 2

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

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