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

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

Answer:

Given :-

• The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively and the time change simultaneously at 8 a.m.

To Find :-

• What is the time change simultaneously again.

Solution :-

First, we have to find the L.C.M of the given time,

✧ 48 = 2 × 2 × 2 × 2 × 3

✧ 72 = 2 × 2 × 2 × 3 × 3

✧ 108 = 2 × 2 × 3 × 3 × 3

Hence, L.C.M of 48, 72 and 108 are,

↪ 2 × 2 × 2 × 2 × 3 × 3 × 3

↪ 432

Then, L.C.M of 48, 72 and 108 is 432.

Now, we know that,

✪ 60 seconds = 1 minutes ✪

If, 60 seconds = 1 minutes

Then, 432 seconds = 432/60

By, doing dividing we get 7 as quotient and 12 as reminder.

Hence, 432 seconds = 7 minutes 12 seconds

Then, the time will be = 8 a.m + 7 minutes 12 seconds

$\therefore$ The time will traffic light change after is 8 : 07 : 12 am .