How many stairs?

Question

There is a flight of stairs. If you go up them 2 at a time, there is one left over. If you go up 3 at a time, there are 2 left over; 4 at a time there are 3 left over; 5 at a time there are 4 left over; 6 at a time there are 5 left over; and 7 at a time there are none left over. How many stairs are there, and could you show me the steps involved in ariving at the answer (no pun intended).

Answer 1

Think of this... if there was one more step, then you would have a number evenly divisible by 2 through 6.

The lowest common multiple of 2, 3, 4, 5 and 6 is:
2 x 2 x 3 x 5 = 60

Now take away one step and see if it is a multiple of 7.
60 - 1 = 59 --> nope
2 x 60 - 1 = 119 --> yes

So the answer is 119:

119 / 2 = 59 r 1
119 / 3 = 39 r 2
119 / 4 = 29 r 3
119 / 5 = 23 r 4
119 / 6 = 19 r 5
119 / 7 = 17 r 0

There's your answer with all the steps shown... :)