Question

In morning walk three persons step off together.Their steps measure 75cm,80cm amd 90cm respectively.What is the minimum distance each should walk so that all can cover the same distance

Answer 1

Answer:

GIVEN: Their steps measure 80 cm, 85 cm, and 90 cm.

We have to find the L.C.M of the measures of their steps to calculate the required distance each should walk.

L.C.M of 80 cm, 85 cm, and 90 cm.

80=2

4

×5

85=17×5

90=2×3

2

×5

L.C.M(80,85,90)=2

4

×3

2

×5×17

=12240cm

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

thus, option A is correct.

Answer 2

The minimum distance each should walk so that all can cover the same distance is 3600 cm.

Given: The steps walked by three persons are 75 cm, 80 cm, and 90 cm.

To Find: The minimum distance each should walk so that all can cover the same distance.

Solution:

• Whenever we are asked to find the minimum or smallest quantity among a set of given values, we should find the LCM of the values given.

• LCM can be found by the prime factorization method or the long division method. Here, we shall use the prime factorization method.

Coming to the numerical, we are given;

The steps walked by three persons are = 75 cm, 80 cm, and 90 cm

Now, to find the minimum distance each of the three people must walk so that all cover the same distance is calculated by finding the LCM of the measure of the steps taken by them.

We shall find the prime factorization,

 75 = 3 × 5 × 5

 80 = 2 × 2 × 2 × 2 × 5

 90 = 2 × 3 × 3 × 5

So, LCM ( 75, 80, 90 ) = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

                                    = 3600

Hence, the minimum distance each should walk so that all can cover the same distance is 3600 cm.

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