Stoplight A changes color every 15 seconds and Stoplight B changes color every 45 seconds. Both stoplights changed color 12 seconds ago. After how many seconds will the stoplights change color at the same time again?

The stoplights will change color after 33 seconds . at the same time again.

Step-by-step explanation:

Given: Stoplight A changes color every 15 seconds and Stoplight B changes color every 45 seconds.

Then, the number of seconds after which they change color at the same time again = least common multiple of 15 and 45.

Since, 15 = 5 x 3 , 45 = 3 x 3 x 5

Least common multiple of 15 and 45. = 3 x 3 x 5 = 45

Since, Both stoplights changed color 12 seconds ago.

So after 45-12 = 33 seconds .

Hence, the stoplights will change color after 33 seconds . at the same time again.