Question

Four lights light up simultaneously at starting and an interval of 6 sec, 12 sec, 15 sec and 20 sec respectively. How many times do they light up together in 2 hours?

1. 120 times
2. 121 times 
3. 191 times 
4. 118 times 

Answer 1

Correct Answer - Option 2 : 121 times 

Given:

Four lights light up simultaneously at starting and an interval of 6 sec, 12 sec, 15 sec and 20 sec respectively.

Concept:

LCM is a multiple of two or more numbers.

Calculation:

LCM of (6, 12, 15, 20) = 60

All 4 lights light up together again after every 60 seconds

Now,

In 2 Hours, they light up together = [(2 × 60 × 60)/60] times + 1 (at the starting) = 121 times

∴ In 2 hours they light up together for 121 times

In these types of questions, we assume that we have started counting the time after the first light-up. Due to this when we calculate the LCM it gives us the lighting up at 2nd time, not the first time. So, we needed to add 1.