<human>:  A party hall has 3 decorative light bulbs; a red light bulb which comes on every 2 seconds, a green one every 3 seconds and a blue one every 4 seconds. If they are put on at the same time, what is the shortest time after which the three bulbs will be on at the same time?
<bot>: How many seconds will the blue light bulb be on? ** 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)
How many seconds will the red light bulb be on? ** 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)
How many seconds will the blue light bulb be on? ** The blue light bulb comes on every 4 seconds so it will be on after 4, 8, 12, 16, 20... seconds (multiples of 4)
What is the shortest time after which all three will be on? ** 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