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?NCERT Class XMathematics - Exemplar ProblemsChapter _Real Numbers

Answer 1

We have to find the LCM of 40 cm, 42 cm and 45 cm to get the required minimum distance. Because we are asked the minimum distance
 Now,
 40 = 2 × 2 × 2 × 5,
 42 = 2 × 3 × 7
45 = 3 × 3 × 5
∴ LCM (40, 42, 45) = 2 × 3 × 5 × 2 × 2 × 3 × 7 = 30 × 12 × 7 = 210 × 12 = 2520

Minimum distance each should walk 2520 cm. so that, each can cover the same distance in complete steps.

Answer 2

To find the minimum distance we have to find the LCM of 40cm,42cm and 45cm

40 => 2 × 2 × 2 × 5 = 2³ × 5

42 = 2 × 3 × 7

45 = 3 × 3 × 5 × 7

=> 840 × 3 = 2520

So the distance to be covered by each = 2520cm