Question

On a morning walk, three persons step off together and their steps measure 40cm ,
42cm and 45cm, respectively. What is the minimum distance each should walk so
that each can cover the same distance in complete steps?

Answer 1

Given :-

Three persons step off together and their steps measure 40cm , 42cm and 45cm, respectively.

To Find :-

What is the minimum distance each should walk so

that each can cover the same distance in complete steps ?

Solution :-

We have to find the L.C.M of the measures of their steps to calculate the required distance each should walk.

L.C.M of 40 cm, 42 cm, and 45 cm :-

☛ 40 = 2 * 2 * 2 * 5 = 2³ * 5

☛ 42 = 2 * 3 * 7

☛ 45 = 3 * 3 * 5 = 3² * 5

LCM = 2³ * 3² * 5 * 7 = 2520 .

Hence, the minimum distance each should walk so that all can cover the same distance in complete steps is 2520.

Answer 2

Solution :-

for minimum Distance we will find LCM of given distance ...

=> 40 = 2 * 2 * 2 * 5

=> 42 = 2 * 3 * 7

=> 45 = 3 * 3 * 5

So, LCM = 2*2*2*3*3*5*7 = 2520

Hence, the minimum distance each should walk so that all can cover the same distance in complete steps is 2520.