Question

Mini is standing in front of three lights which are turning on and off. She observes the lights lit up after every 10, 12 and 15 minutes respectively. If all the lights lit up together for the last time at 1 P. M. At what time will they lit up together again?

• A. 1:45 PM
• B. 2 PM
• C. 3 PM
• D. 5 PM

Answer 1

The correct option is B 2 PM

The lights are changing after 10, 12 and 15 minutes respectively.
They have to lit up together.
So, in this case, we have to find out a number which is divisible by 10, 12 and 15 respectively. That is, we have to find L.C.M here.
So,
Prime factors of $10=1\times 2\times 5$.
Prime factors of $12=1\times 2\times 2\times 3$.
Prime factors of $15=1\times 3\times 5$.
So, the L.C.M of 10, 12 and 15 will be = 2 x 2 x 3 x 5 = 60 minutes = 1 hour.
The lights lit up last at 1 P.M. So, next they will lit up at
= 1 P. M.+ 1 hour
= 2 P. M.