a) What is the least number that is divisible by each of the single-digit positive integers?

b) When you multiply all the integers from 1 to 100, how many zeroes appear at the end of the answer?

c) There are 100 light switches on the wall of a corridor, all in the off position. 100 people pass along the corridor flicking switches. The first person flicks every switch, the second flicks every second switch (starting with the second), the third every third switch (starting with the third), and so forth. By the time all 100 have passed through, how many lights are on?