Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again? 

Dear Student

Red bulb flash at an interval of 80 seconds
Green bulb flash at an interval of 90 seconds
​​​​​​Yellow bulb flash at an interval of 110 seconds

Now, take LCM of (80,90,110)  
 

Prime factorization of the numbers:

80 = 2 × 2 × 2 × 2 × 5
90 = 2 × 3 × 3 × 5
110 = 2 × 5 × 11

LCM(80, 90, 110)
= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 11
= 7920 seconds
= $\frac{7920}{60} = 132 minutes =2 hours 12 minutes$

Given that they have flashed together at 8:00 am

Now they will flash together at 10:12 am.


​​​​​​​Regards