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

To find the minimum distance each person should walk so that they can cover the distance in complete steps, we need to find the least common multiple (LCM) of their step lengths. The LCM is the smallest distance that is divisible evenly by all three step lengths.

Step lengths: 80 cm, 85 cm, and 90 cm.

To find the LCM, we can factor each of these step lengths into their prime factors:

80 cm = 2^4 * 5
85 cm = 5 * 17
90 cm = 2 * 3^2 * 5

Now, we can find the LCM by taking the highest power of each prime factor that appears in any of the step lengths:

LCM = 2^4 * 3^2 * 5 * 17

LCM = 16 * 9 * 5 * 17

LCM = 12240 cm

So, the minimum distance each person should walk to cover the distance in complete steps is 12,240 cm for each of them.