The blue light bulb comes on every 2 seconds so it will be on after 2, 4, 6, 8, 10, 12, 14... seconds (multiples of 2)
The red light bulb comes on every 3 seconds so it will be on after 3, 6, 9, 12, 15, 18... seconds (multiples of 3)
The blue light bulb comes on every 4 seconds so it will be on after 4, 8, 12, 16, 20... seconds (multiples of 4)
The shortest time after which all three will be on is 12 seconds which is the least common multiple of the set of multiples.
#### 12