Question

The traffic lights at three different road crassings change after every 48 sec,72sec,108 sec.If they start changing simutaneously ,at 10 a.m,after how much time will they change again simultaneosly

Answer 1

You have to find the l.C.M of 48,72 and 108 = 432.
Therefore, they will start together at 10:7.2

Answer 2

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

If the traffic lights change simultaneously at 10 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:

• 10 am + 7 minutes 12 seconds
• 10 : 07 : 12 am