Question

On a morning walk three persons step off together, their steps measure 75 cm, 82 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?​

Answer 1

Answer:

2520

Step-by-step explanation:

In this question, we are given a measurement of each step to cover the same distance. The minimum distance each should walk will be the lowest common multiple of each of their steps. Hence each person should walk a minimum distance of 2520cm in complete steps.

Answer 2

To find the minimum distance the three should walk so that all can cover the same distance in whole steps, we need to find the lowest common multiple of the measures of the steps.

Given:

The measures of the steps of the three people: 75 cm, 82 cm and 90 cm.

To find:

The L.C.M of the numbers 75, 82 and 90.

Solution:

Finding L.C.M through prime factorization:

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 75 , 82 , 90} \\ \cline{1-2} \tt 3 & \sf { 75 , 41 , 45 } \\ \cline{1-2} \tt 3 & \sf{ 25 , 41 , 15} \\ \cline{1-2} \tt 5 & \sf{ 25 , 41 , 5} \\ \cline{1-2} \tt 5 & \sf{ 5 , 41 , 1}\\ \cline{1-2} \tt 41 & \sf{ 1 , 41 , 1}\\ \cline{1-2} & \sf{ 1 , 1 , 1} \end{array}}$

$\sf{LCM\:=\:2\times3\times3\times5\times5\times41\:=18450}$

Therefore, the minimum distance each should walk so that each can cover the same distance in complete steps is 18450 cm or 184.5 m.