Question

The traffic lights at three different road crossings change after
every 48 seconds, 72 seconds and 108 seconds respectively. If they
change simultaneously at 7 am, at what time will they change
simultaneously again?
​

Answer 1

Step-by-step explanation:

find the prime factor

48=24×33

72 =23×32

its answer is 8:07:12am

Answer 2

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

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