question_answer 1)

Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm, respectively. What is the minimum distance each should cover, so that all can cover the distance in complete steps?

Answer:

                Here, the required minimum distance will be equal to LCM of measures of their steps, because, the minimum distance each boy should walk must be the least common multiple of the measure of their steps. So, we have to find out the LCM of 63, 70 and 77 cm. i.e.                      2 63,70,77 3 63,35,77 3 21,35,77 5 7,35,77 7 7,7,77 11 1,1,11 1,1,1 \[\therefore \] LCM of 63, 70 and\[77=2\times 3\times 3\times 5\times 7\times 11=6930\] Hence, required minimum distance = 6930 cm