In a morning walk three persons steps off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that they can cover the distance in complete steps?

Given: The steps measure 80 cm, 85 cm and 90 cm respectively

To find: the minimum distance each should walk so that they can cover the distance in complete steps

Solution: 

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 $ \times $ 5

85 = 17 $ \times $ 5

90 = 2 $ \times $ 3 $ \times $ 3 $ \times $ 5

L.C.M of 80, 85 and 90 = 2⁴ $ \times $ 3 $ \times $ 3 $ \times $ 5 $ \times $ 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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Updated on: 10-Oct-2022

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