at a school there is1000 lockers. Outside there are 1000 students waiting to open and close doors. student 1 opens all 1000 doors. student 2 closes all the multiple of 2 doors, student three closes all the multiple of 3 doors. (the doors already closed he reopen. student 4 does the same for multiples of 4 etc until all 1000 students go. Which lockers are left open? I think it is all the lowest common multiples, but I do not know how to explain it.

Question

anonymous · Answer

Think about how many times a specific locker gets opened and closed.  Say locker number 50.

It will get touched by the 1st, 2nd, 5th, 10th, 25th, and 50th kids.

What do those numbers represent?