A liquid crystal display consists of red, green, and blue LED bulbs. The lighting cycle rules for each color bulb are as follows: Red: ``On for 3 seconds, then off for 1 second, then on for 2 seconds'' Green: ``On for 6 seconds, then off for 2 seconds'' Blue: ``On for $k$ seconds, then off for ($15 - k$) seconds'', where $k$ is a positive integer. If at a certain moment all three colors of bulbs simultaneously begin their respective cycles, and the display always has lights on, with the switching time between on and off being negligibly short, then the minimum value of $k$ is
A liquid crystal display consists of red, green, and blue LED bulbs. The lighting cycle rules for each color bulb are as follows:
Red: ``On for 3 seconds, then off for 1 second, then on for 2 seconds''\\
Green: ``On for 6 seconds, then off for 2 seconds''\\
Blue: ``On for $k$ seconds, then off for ($15 - k$) seconds'', where $k$ is a positive integer.\\
If at a certain moment all three colors of bulbs simultaneously begin their respective cycles, and the display always has lights on, with the switching time between on and off being negligibly short, then the minimum value of $k$ is