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 and complete steps?

Answer 1

Since the three persons start walking together.

$\therefore$, The minimum distance covered by each of them in complete steps $=$ LCM of the measures of their steps

$=LCM(40,42,45)$

$40=2\times 2\times 2\times 5=2^3\times 5$

$42=2\times 3\times 7$

$45=3\times 3\times 5=3^2\times 5$

$\Rightarrow LCM(40,42,45)=2^3\times 3^2\times 5\times 7=2520$

$\Rightarrow$ Each person should walk a minimum distance of $2520$ cm in complete steps.