Question

On a morning walk, three persons step off together and their steps measure 90 cm, 120 cm and 130cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?NCERT Class XMathematics - Exemplar ProblemsChapter _Real Numbers

Answer 1

Given :  On a morning walk, three persons step off together and their steps measure 90 cm, 120 cm and 130 cm respectively.  

To find : the minimum distance each should walk so that each can cover the same distance in complete steps

Solution :

Let say Distance Covered  = d

Then Step walked  are  d/90    , d/120  & d/130

=> d = 90A   = 120B  = 130C

=> d must be minimum the LCM of 90 , 120 & 130

90 = 2 * 3 * 3 * 5

120 = 2 * 2 * 2 * 3 * 5

130 = 2 * 5 * 13

LCM = 2 * 2 * 2 * 3 * 3 * 5 * 13

= 4680

Hence minimum distance need to Walk = 4680 cm   = 46.8 m