In a morning walk three persons step off together. their steps measure 80 cm , 85 cm , 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps ?

Given :

The steps of three persons measure 80 cm, 85 cm and 90 cm.

To find :

We have to find the minimum distance each should walk so that all can cover the same distance in complete steps.

Solution :

If they step off at the same time the minimum distance each should walk so that all can cover the same distance in complete steps is the LCM of 80,85 and 90.

LCM of 80,85 and 90 is,

$80 = 2\times2\times2\times2\times5$

$85 = 5\times17$

$90 = 2\times3\times3\times5$

LCM of 80,85 and 90 $= 2\times2\times2\times2\times3\times3\times5\times17 = 12240$

The minimum distance each should walk is $12240 cm = 122.4 m$.

Number of steps taken by 1st person $= \frac{12240}{80} = 153$.

 Number of steps taken by 2nd person $= \frac{12240}{85} = 144$.

Number of steps taken by 3rd person $= \frac{12240}{90} = 136$.

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Updated on: 10-Oct-2022

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