In a morning walk three persons step off together, their steps measure 80cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?
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SOLUTION :
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 i.e. 80 cm, 85 cm, and 90 cm, to calculate the required distance each should walk.
L.C.M of 80 cm, 85 cm, and 90 cm.
80 = 2⁴ x 5
85 = 17 x 5
90 = 2 x 3 x 3 x 5
L.C.M of 80, 85 and 90 = 2⁴ x 3 x 3 x 5 x 17
L.C.M of 80, 85 and 90 = 12240 cm
Hence, the minimum distance each should walk so that all can cover the same distance in complete steps is 12240 cm.
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Solutions :-
Given :
Three persons step off together, their steps measure 80cm, 85 cm and 90 cm respectively.
Find is the minimum distance each should walk so that he can cover the distance in complete steps :-
To find the minimum distance we have to find the LCM of 80, 85 and 90,
Prime Factors :-
80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5
85 = 5 × 17
90 = 2 × 3 × 3 × 5 = 2 × 3² × 5
LCM of 80, 85 and 90 = 2⁴ × 3² × 5 × 17 = 12240
Hence,
The minimum distance each should walk so that he can cover the distance in complete steps = 12240 cm
Given :
Three persons step off together, their steps measure 80cm, 85 cm and 90 cm respectively.
Find is the minimum distance each should walk so that he can cover the distance in complete steps :-
To find the minimum distance we have to find the LCM of 80, 85 and 90,
Prime Factors :-
80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5
85 = 5 × 17
90 = 2 × 3 × 3 × 5 = 2 × 3² × 5
LCM of 80, 85 and 90 = 2⁴ × 3² × 5 × 17 = 12240
Hence,
The minimum distance each should walk so that he can cover the distance in complete steps = 12240 cm
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