Lcm And Hcf

Step 1: Finding the Least Common Multiple (LCM)
The first step is to find the Least Common Multiple (LCM) of the given times, 48 s, 72 s, and 108 s, to determine when the lights will all change simultaneously again.
- The prime factorization of 48 is: 48 = 2⁴ × 3
- The prime factorization of 72 is: 72 = 2³ × 3²
- The prime factorization of 108 is: 108 = 2² × 3³
The LCM is found by taking the highest power of each prime factor: LCM(48, 72, 108) = 2⁴ × 3³ = 16 × 27 = 432 seconds
Step 2: Converting Seconds to Time
Now that we know the LCM is 432 seconds, we need to add this time to the initial time (8:20:00 h).
432 seconds is equivalent to: 432 seconds = 7 minutes and 12 seconds
Step 3: Adding Time
Adding 7 minutes and 12 seconds to 8:20:00 h: 8:20:00 + 7:12 = 8:27:12
Step 4: Conclusion
Thus, the traffic lights will change simultaneously again at 8:27:12 h.