Question

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

Answer 1

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Required 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

➙ 08 : 07 : 12 am. (Answer)

Answer 2

Step-by-step explanation:

Given

The traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.

So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

LCM of 48, 72 and 108 = 432

So after 432 seconds they will change simultaneously

We know that

60 seconds = 1 minute

so on dividing 432 / 60 we get 7 as quotient and 12 as reminder

Hence, 432 seconds = 7 min 12 seconds

∴ The time = 7 a.m. + 7 minutes 12 seconds

Hence the lights change simultaneously at 7:07:12 a.m