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?
Answers
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)
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