Question

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?

Answer 1

Hint: Here first we will check the units of the lengths of the steps and then we will take the LCM of the three quantities by writing the factors of each length using the prime factorization method.
The LCM will give the minimum distance that each of the three persons should cover in order to cover the same distance.

Complete step-by-step answer:
The measure of steps are 80 cm, 85 cm and 90 cm.
Now since the units of each of the length is the same hence we can take the LCM of these terms.
So first we will factorize these terms into their prime factors using the prime factorization method.
Let us first write the factors of 80:-
\[80 = 2 \times 2 \times 2 \times 2 \times 5\]
Now let us factorize 85:-
\[85 = 17 \times 5\]
Now let us factorize 90:-
\[90 = 2 \times 3 \times 3 \times 5\]
Now we will take the LCM
We know that LCM is the least common factor of three of the numbers.
Hence, LCM of the three numbers is:-
\[LCM = 2 \times 2 \times 2 \times 2 \times 5 \times 3 \times 3 \times 17\]
Solving it we get:-
\[LCM = 12240cm\]
Converting it into meter we get:-
\[LCM = 12240cm = 122m40cm\]

Hence, the minimum distance each person should walk so that all can cover the same distance in complete steps is 12240 cm. or 122m 40cm.

Note: Students should note that we need to factorize the numbers into prime factors in order to get the correct LCM of the given numbers.
Also, LCM is the product of all the factors such that the common factor to three of the numbers is multiplied once.
We use LCM to find the minimum value and HCF to find the maximum value.