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?

• A. $1680$
• B. $1800$
• C. $75600$
• D. $2520$

Answer 1

The correct option is D $2520$

The minimum distance that all $3$ should walk is the L.C.M. of $40,42,45$

Since

$40=2\times 2\times 2\times 5$
$42=2\times 3\times 7$
$45=3\times 3\times 5$

Therefore,

L.C.M. of $40,42,45=2\times 2\times 2\times 3\times 3\times 5\times 7$
$=2520$
$=2520$ cm