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!

Can anyone help?

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

Or just multiply 12....... 12, 24, 36 etc, until you come to a number that is divisible by 9 and 6 as well.

Thanks for the replies. I think it's probably easiest for a 10 year old to go through the 12 times table and check when they find a multiple of the other numbers then and leave factoring until they are a bit older.

If you do the 12 times table 6 is already going to be a factor so you are just looking for a multiple of 9.

Good point. That makes it easier still. Thanks

can someone please explain how to explain this question to 10 yo? thank you