NUKMERACY
posted by DJAZIA .
THERE ARE 3 LIGHT HOUSES,THE FIRST ONE SHINE FOR 3 SECONDS, THEN IS OFF FOR 3 SECONDS.the 2 one shine for 4 seconds then is off for 4 seconds.the 3 one shine for 5 seconds,then is off for 5 seconds.all thr 3 lights have just come together.when is the first time that all the three lights will come off?.when is the next time that all the three lights will come on at the same moment?

The period between the beginning of a "shine" is 6 seconds for #1, 8 seconds for #2 and 10 seconds for #3. the lowest common multiple of those numbers is 2*3*2*2*5 = 120 seconds. That is when they will come ON together for the next time.
When they come OFF together is more complicated. #1 goes off at t = 3, 9, 15, 21, 27, etc s. #2 goes off at 4, 12, 20, 28, 36.. s. One set of number is odd and the other even. The "off" times can never coincide.
Maybe another teacher will prove me wrong about this