Question

Question 12
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?

Answer 1

The minimum distance that they need to walk is given by the LCM of 40, 42 and 45.
$40=2\times 2\times 2\times 5$
$42=2\times 3\times 7$
$45=3\times 3\times 5$
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 is 2520 cm so that each can cover the same distance in complete steps.