**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?

**Solution:**

GIVEN: In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm.

TO FIND: minimum distance each should walk so that all can cover the same distance in complete steps.

The distance covered by each of them is required to be same as well as minimum. The required distance each should walk would be the L.C.M of the measures of their steps i.e. 80 cm, 85 cm, and 90 cm,

So we have to find the L.C.M of 80 cm, 85 cm, and 90 cm

$80=2^{4} \times 5$

$85=17 \times 5$

$90=2 \times 3^{2} \times 5$

L.C.M of 80,85 and $90=2^{4} \times 3^{2} \times 5 \times 17$

$=12240 \mathrm{~cm}$

Hence minimum $=12240 \mathrm{~cm}$ distance each should walk so that all can cove the same distance in complete steps