Question

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

Answer 1

We have to find the LCM of 80 cm, 85 cm, and 90 cm.
Prime factorisation of 80 = 2 × 2 × 2 × 2 × 5
Prime factorisation of 85 = 5 × 17
Prime factorisation of 90 = 2 × 3 × 3 × 5

∴ Required LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 17 = 12,240
∴ Required minimum distance = LCM of 80 cm, 85 cm, and 90 cm
= 12,240 cm
= 122 m 40 cm (since 1 m =100 cm)