Here we go again wrote:
Three roadside flashing beacons are all switched on at the same time. One flashes every 6 seconds, one every 9 seconds and the third every 12 seconds. How many seconds after being switched on do they flash at the time?
I am aware you could do it like this:
6 second beacon: 6, 12, 18, 24, 30, 36
9 second beacon: 9, 18, 27, 36
12 second beacon: 12, 24, 36
Hence answer 36 seconds.
However, I am sure these questions get much harder so that it is impossible to write it out long-winded like this. I know there is a rule for these types of problems but can't for the life of me remember what it is!
You want the smallest number that all of these numbers divide into. You could do it by factorizing:
6 = 2x3
9 = 3x3
12 = 2x2x3
so a common multiple must have all these factors:
2x2x3x3 = 36