Question

I climb half the steps in a staircase. Next, I climb one-third of the remaining steps. Then I climb one-eight of the rest and stop to catch my breath. What is the least possible number of steps in the staircase?

Answer 1

Given parameters:

   First sets of staircase  = $\frac{1}{2}$

   Next sets  = $\frac{1}{3}$

    Third sets  = $\frac{1}{8}$

Unknown:

The least possible number of steps =?

Solution:

The least possible number of steps will be the lowest common multiples of these sets of steps.

We want fractions that will give whole numbers because realistically, one cannot take half a step of a step.

 So, the number of steps must be a multiple of denominators of the fractions given.

   Denominators are 2 , 3 and 8

     Their least common multiple is 24;

    This the lowest number by which 2, 3 and 8 can all divide.

So, the least number is 24 steps