Question:
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively.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 LCM of 40 cm, 42 cm and 45 cm to get the required minimum distance.
For this, $40=2 \times 2 \times 2 \times 5$,
$42=2 \times 3 \times 7$
and $45=3 \times 3 \times 5$
$\therefore$ $\operatorname{LCM}(40,42,45)=2 \times 3 \times 5 \times 2 \times 2 \times 3 \times 7$
$=30 \times 12 \times 7=210 \times 12$
$=2520$
Minimum distance each should walk 2520 cm. So that, each can cover the same distance in
complete steps.