The stoplights will change color after 720 seconds. at the same time again.
Given: Stoplight A changes color every 45 seconds and Stoplight B changes color every 80 seconds.
The Least common multiple (LCM) will include one copy of the common factor and all of the unique factors.
Then, the number of seconds after which they change color at the same time again = least common multiple of 45 and 80.
Since, 45 = 5 x 3 x 3 , 80 = 5 x 2 x 2 x 2 x 2
A least common multiple of 45 and 80. = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720
Since both stoplights changed color just now.
Hence, the stoplights will change color after 720 seconds. at the same time again.
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