# in a morning walk, three persons step off together. their steps measure 80 cm, 85 cm and 90 cm respectively. what is the minimum distance each should walk so that all can cover the same distance in complete steps?

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

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

Byju's Answer Standard X Mathematics

Applications of HCF & LCM in Real-World Problems

In a morning ... Question

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

Open in App Solution

**GIVEN:**In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm.

**TO FIND:**minimum distance each should walk so that all can cover the same distance in complete steps.

The distance covered by each of them is required to be same as well as minimum. The required distance each should walk would be the L.C.M of the measures of their steps i.e. 80 cm, 85 cm, and 90 cm,

So we have to find the L.C.M of 80 cm, 85 cm, and 90 cm.

80 = 24 x 5 85 = 17 x 5 90 = 2 x 3 2 x 5

L.C.M of 80, 85 and 90 = 24 x

3 2 x 5 x 17 = 12240 cm

Hence minimum 12240 cm distance each should walk so that all can cover the same distance in complete steps.

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SIMILAR QUESTIONS

**Q.**In a morning walk, three friends step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. Find the minimum distance each friend should walk so that all can cover the same distance in complete steps.

**Q.**On a morning walk, three persons step off together and their steps measure

40 cm, 42 cm and 45

cm respecting. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

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Applications of HCF & LCM in Real-World Problems

Standard X Mathematics

Click here👆to get an answer to your question ✍️ In a morning walk three persons step off together, their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?

Question

**A**

## 122m 40cm

**B**

## 120m 44cm

**C**

## 120m 40cm

**D**

## 124m 44cm

Medium Open in App Solution Verified by Toppr

Correct option is A)

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.

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## In a morning walk three persons step off together Their steps measure 80cm 85cm and 90cmrespectively...

Free solutions for R D Sharma Mathematics solutions - Class 6 Chapter 3 - Playing with numbers Playing with numbers Exercise 2.10 question 6. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## RD Sharma Solutions Class 6 Mathematics Solutions for Playing with numbers Exercise 2.10 in Chapter 2 - Playing with numbers

Prev Question 6 Next

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

Answer:

Prime factorization of

80 = 2 × 2 × 2 × 2 × 5

85 = 5 × 17 90 = 2 × 3 × 3 × 5

So the required LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 17 = 12240

**Hence, the required minimum distance each should walk = LCM of 80cm, 85cm and 90cm = 12240 cm = 122m 40cm.**

**Video transcript**

hello students welcome to lido homework my name is nira nirola and in today's q a video we are going to solve a word problem so let's read the question carefully first in a morning walk three person steps off together their steps measures 80 centimeter 50 85 centimeter and 90 centimeter respectively what is the minimum distance it should work so that he can cover the distance in complete steps so this is the question right now let us try to visualize this question so we have the first person here and the step that he takes right the steps that he takes is 80 centimeter now we have the second person here let's say he's a little bit taller and this distance covered by him in one step is 85 centimeter now let us take the third person here he is even taller so the distance covered by him in one step is 90 centimeter so these are the steps taken by each person right now what is the question asking us it is asking us to find the minimum distance it should work so that he or she or they can cover the distance in complete steps all right so now what we are supposed to do we are not uh we are we will not allow this three person to take any half steps right he shouldn't uh in next time he shouldn't take 40 centimeter he should continue to keep on taking 80 centimeter similarly this guy also in each step he should cover 85 centimeter of distance similarly the third person also should cover 95 90 centimeter of the distance in each step so they are not allowed to reduce the distance of their steps okay now we are supposed to find the minimum distance right the minimum distance so that each one of them will reach without having to reduce the distance of their step so basically what are we supposed to do we are supposed to find some multiple of 80 another multiple of 85 and multiple of 90 and that multiple should be the common multiple of 80 also for 85 also for 90 also right there should be the common multiple and further since the question is asking us the minimum distance it should be the least common multiple so where i'm going to i'm supposed to find the lcm of 80 85 and 90 to get the answer so let us try to find the lcm now yes we'll just draw a straight line quickly let us start so yeah okay so let us find the lcm of 80 85 and 90 centimeter and that will give us the answer that will give us the minimum distance right so the solution will be to find the lcm of 80 85 and 90 so let us make use of prime factorization to find the lcm two forties is eighty two twenty zero is forty two tanza is twenty and 2 5 is 10. similarly for 85 5 wonza is 5 5 7 is 85 similarly for 19 245 is 90 3 1 3 3 5's are 15 3 5 j is 15 so we will we can write 80 as 80 can be written as 2 into 2 into 2 into 2 into 5 right similarly 85 can be written as 5 into 17 right 5 into 17 and 90 can be written as 2 into 3 into 3 into 5 so let us see what is common here so basically this five right these five these five and this five they are common in all the three cases further this two and these two are common in two cases right now let us find the lcm it will be easy to find the lcm so lcm is 5 into 2 i have taken only the common terms now let us take the leftovers right into 2 into 2 into 2 in this case into 17 and into 3 into 3 so 5 into 2 will give me 10 10 into 2 will give me 20 20 into 2 will give me 40 14 into 2 will give me 80. so 80 into 17 into 9 right so let us quickly multiply 80 into 17 first so when we multiply 80 into 17 into nine yes seven zeros is zero seven eight zero is fifty six one zero zero zero one eight za is eight right so zero six 1 3 6 0 so yes 18 into 17 is giving me 1 3 6 0 and i'm supposed to multiply this with 9 correct so let us quickly multiply this with nine nine zeros are zero nine six zero is fifty four five in nine nine three is twenty seven twenty eight twenty nine thirty thirty one thirty two three in hand nine one zero nine ten eleven twelve yes 9119 so they should cover one two two four zero yeah so this is the lcm guys therefore what can we conclude the minimum distance it should work the minimum distance each should work it should work yes one two two four zero centimeters that's it guys so that's it for today's q a video q a video if you have any doubt please post it in the comment below and if you like the video and for such upcoming videos do subscribe to lido bye guys take care

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