On a morning walk three person...

On a morning walk, three persons step off together and their steps measure 40cm, 42cm and 45cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
A. 1680
B. 1800
C. 75600
D. 2520

Answer

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Hint: In this question, we are given a measurement of each step to cover the same distance. The minimum distance each should walk will be the lowest common multiple of each of their steps.

Complete step-by-step answer:

Measure of steps of three persons = 40, 42, 45 cm

Minimum distance covered by each of them in complete steps = LCM of measure of their steps = LCM of (40, 42, 45)

40 = $2 \times 2 \times 2 \times 5$

42 = $2 \times 3 \times 7$

45 = $3 \times 3 \times 5$

LCM (40, 42, 45) = $2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7$

=2520

Hence each person should walk a minimum distance of 2520cm in complete steps.

Note: For these types of questions, remember the concept of LCM and HCF. LCM is the least number which is divided by the given numbers and HCF would be the largest of all numbers which divides the given numbers.