Question

The traffic lights at three different road crossings change after every
48 seconds, 72 seconds and 108 seconds respectively. If they all change
simultaneously at 8 a.m. then at what time will they again change
simultaneously?​

Answer 1

$\huge{\underline{\underline{\huge{\bold{AnsweR \: :-}}}}}$

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.

Then, finding the 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 is the product of highest degrees of factors. Then, 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

➙ 8 am + 7 minutes 12 seconds➙ 08 : 07 : 12 am. (Answer)

Answer 2

$\green{ \fcolorbox{grey}{grey}{ \checkmark \: \textsf{Verified \: answer}}}$

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