The traffic lights at three different road crossings change after 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 am, at what time will they change simultaneously again.

To find out when the traffic lights will change simultaneously again, we need to determine the least common multiple (LCM) of the three time intervals: 48 seconds, 72 seconds, and 108 seconds.

Finding the LCM

We can start by breaking down each number into its prime factors:

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

Calculating the LCM

The LCM is found by taking the highest power of each prime factor:

• For 2: the highest power is 2⁴
• For 3: the highest power is 3³

Thus, the LCM is:

LCM = 2⁴ × 3³ = 16 × 27 = 432 seconds.

Converting Seconds to Minutes

Now, we convert 432 seconds into minutes:

432 seconds ÷ 60 = 7 minutes and 12 seconds.

Finding the Next Simultaneous Change Time

If the lights change simultaneously at 7:00 AM, we add 7 minutes and 12 seconds:

7:00 AM + 7 minutes and 12 seconds = 7:07 AM and 12 seconds.

Final Answer

The traffic lights will change simultaneously again at 7:07:12 AM.