Question

The traffic lights at three different road crossing changes after every 48 seconds, 72 seconds and 108 seconds. if they change simultaneously at 6 a.m., at what time will they change simultaneously again ​

Answer 1

Answer:

• They will change again at 06:07:12 a.m.

Step-by-step explanation:

Given that:

• The traffic lights at three different road crossing changes after every 48 seconds, 72 seconds and 108 seconds.
• They change simultaneously at 6 a.m.

To Find:

• At what time will they change simultaneously again?

Concept:

• First we have to find the LCM of the interval of traffic light of all three different road crossing and after we will add the time the value which we get from the LCM to 6 a.m. and then we get the required answer.

Finding the LCM:

By prime factorisation.

• Factors of 48 = 2⁴ × 3
• Factors of 72 = 2³ × 3²
• Factors of 108 = 2² × 3³

Lowest common multiple of 48, 72 and 108 is 2⁴ × 3³ = 432

Hence,

• After 432 seconds they will change simultaneously again.

Converting 432 seconds into minutes and seconds:

• [1 minute = 60 seconds]

= 432 seconds

= 420 seconds + 12 seconds

= 420/60 minutes + 12 seconds

= 7 minutes + 12 seconds

= 7 minutes and 12 seconds

Finding the time:

First changes at 6 a.m.

Second changes after 7 minutes and 12 seconds.

or, 6:00:00 + 0:07:12 = 06:07:12 a.m.

So,

• At 06:07:12 a.m. they will change simultaneously again.

Answer 2

Given :-

The  traffic lights at three different road crossing changes after every 48 seconds, 72 seconds and 108 seconds. if they change simultaneously at 6 a.m.,

To Find :-

At what time will they change simultaneously again

Solution :-

Factors of 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

Factors of 72 =  2 × 2 × 2 × 3 × 3 = 2³ × 3²

Factor of 108 =  2 × 2 × 3 × 3 × 3 = 2² × 3³

LCM = 432

Now

They will rank after 7 minutes 12 sec