Three lights are turning green at an interval of every 24, 30, and 42 seconds.
Let three lights are L1, L2 & L3:
L1 is turning green at (interval in seconds): 24, 48, 72, 96, ...
L2 is turning green at (interval in seconds): 30, 60, 90, 120, ...
L1 is turning green at (interval in seconds): 42, 84, 126, 168, ...
If they start at the same time, they will turn green at the same time again in:
LCM of 24, 30, 42
After 840 seconds or 14 minutes.