<PRE><B>Question 104964</B>
Convert all of the time to seconds so you have the same units. 
P1 = 45 seconds
P2 = 2 minutes = 120 seconds
P3 = 1 1/4 minutes = 75 seconds
This problem is similar to finding the least common multiple (LCM) for a fraction. 
Break the numbers into their prime factors.
Find the largest powers of each prime factor. 
Calculate the product of all of the largest powers of the prime factors. 
{{{45=highlight(3^2)*5^1}}}
{{{120=highlight(2^3)*3^1*5^1}}}
{{{75=3^1*highlight(5^(2))}}}
The prime factors are 2,3,and 5 with the highest power highlighted. 
{{{LCM = highlight(2^3)*highlight(3^2)*highlight(5^2)}}}
{{{LCM = 8*9*25}}}
LCM = 1800 seconds. So every 1800 seconds after 8:35 PM, the lights will all blink simultaneously. 
1800 seconds = 30 minutes
8:35 PM + 30 minutes = 9:05 PM. </PRE>