In a morning walk three persons step off together their steps measure 80cm,85cm and 90cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

The minimum distance each should walk to cover the same distance is 12240 cm

Step-by-step explanation:

The minimum distance each should walk so that all can cover the same distance in complete steps is the same as the Lowest Common Multiple (LCM) of the three numbers, which is the least integer that is divisible by each of the three numbers.

To find the LCM, we will first find the lowest multiples of each of the numbers

80 ⇒ (2) × 2 × 2 × 2 × (5)

85 ⇒ 17 × (5)

90 ⇒  (2) × 3 × 3 × (5)

Note: in finding LCM, the numbers common to at least 2 (in bracket), out of the three terms is written just once.

∴ LCM = 2 × 2 x 2 × 2 × 3 × 3 × 5 × 17

= 16 x 9 x 85

= 12240 cm

Therefore, the minimum distance each should walk to cover the same distance is 12240 cm