On a morning walk, three persons step off together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps​?

Given: Steps of three persons measure 30 cm, 36 cm and 40 cm respectively.

To find: Here we have to find the minimum distance each should walk so that he can cover the distance in complete steps.

Solution:

Required distance will be the LCM of the measure of steps of each person.

Calculating the LCM of 30, 36 and 40 using prime factorization method:

Writing the numbers as a product of their prime factors:

Prime factorisation of 30:

• $2\ \times\ 3\ \times\ 5\ =\ 2^1\ \times\ 3^1\ \times 5^1$

Prime factorisation of 36:

• $2\ \times\ 2\ \times\ 3\ \times\ 3\ =\ 2^2\ \times\ 3^2$

Prime factorisation of 40:

• $2\ \times\ 2\ \times\ 2\ \times\ 5\ =\ 2^3\ \times\ 5^1$

Multiplying the highest power of each prime number:

• $2^3\ \times\ 3^2\ \times\ 5^1\ =\ 360$

LCM(30, 36, 40)  $=$  360

Which means required distance  $=$  360 cm  $=$  3 m 60 cm (as, 100 cm  $=$  1 m)  

So, the minimum distance each should walk so that each can cover the distance in complete steps is 360 cm or 3 m 60 cm.

Tutorialspoint

Updated on: 10-Oct-2022

229 Views

Kickstart Your Career

Get certified by completing the course

Get Started