Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.21)

21. 

The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

[A]. 15 cm
[B]. 25 cm
[C]. 35 cm
[D]. 42 cm

Answer: Option C

Explanation:

Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.


Priz said: (Dec 27, 2010)  
How come 35?

I need explanation.

Aparna said: (Dec 27, 2010)  
Don't worry its very easy

Whenever in the question,words like greatest or measurement or length comes,it is an HCF question
look at the options
the answers are in cm,so convert in cm all the values

e.g:
3m 85cm

1m=100cm
3m=?

we get,300cm
just add 85 in this,but don't do mutiplication
i:e
300+85=385

similarly,do with other nos.
and further find its HCF

Raviteja said: (Aug 22, 2011)  
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm.
385)700(1
385
---
315)385(1
315
---
70)315(4
280
---
35)70(2
70
--
x

35)1295(37
1295
----
X
----
i.e., H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

111 said: (Sep 11, 2011)  
Thanks Ravireja

111 said: (Sep 11, 2011)  
Thanks raviteja

Nikhil said: (Mar 4, 2014)  
Why it is HCF? why not LCM?

Please explain.

145 said: (Apr 2, 2014)  
As we need to find out greatest possible length as mentioned in the queue. We need to find out HCF and not LCM.

146 said: (Oct 7, 2014)  
Please give me the prime factors of 1295.

Nareshbora said: (Oct 24, 2014)  
Easy process to find HCF is

7m = 7*100 = 700cm.

3m85cm = 3*100+85 = 385cm.
12m95cm = 1200+95 = 1295cm.

Given lengths in cm are 700, 385, 1295

Now 700-385 = 315.

1295-385 = 910.
1295-700 = 595.

Factors for 315 = 7*5*3*3.

910 = 7*5*2*13.
595 = 7*5*17.

Common Highest factor is 7*5 = 35.

So, answer is 35.

Gopi Krishna said: (Oct 29, 2014)  
How we can find factors for such numbers?

Renuka said: (Jun 8, 2015)  
Thank you friends.

Pritam said: (Nov 17, 2015)  
Could not understand why HCF not LCM?

Vipin said: (Jan 19, 2016)  
Why 85 cm is considering to find HCF?

Ramboo said: (Feb 23, 2016)  
Because question says greatest possible length.

Sindhuroyal said: (Mar 4, 2016)  
Firstly we have to find two number which is low among three numbers. So we have to take 385,700., in this two numbers 700 is divided by 385.
385)700(1
385
_______
315)385(1
315
_____
70)315(4
280
_______
35)70(2
70
_____
0
The above two numbers is divided till we get remainder is 0. Then last number 35 is need to taken. We have other number which is 1295.
35)1295(37
105
_____
245
245
_____
0
_____
So that, 35 is answer guys.

Arun said: (May 10, 2016)  
Good explanation, Thank you friends.

Abhishek Chaudhary said: (Jun 10, 2016)  
Please tell me one thing. When we have to take LCM and HCF?

I am confused about this.

Tessa said: (Jun 29, 2016)  
We need a length which can be used to measure the three given Lengths.

So it should be a common factor of all three numbers nd it should be the greatest also. So it's clearly highest common factor or HCF.

Aditya (Dada) said: (Jul 13, 2016)  
How to decide whether to take hcf or lcm for such sums?

Mounika said: (Dec 20, 2016)  
Thank you for the Excellent explanation @Aparna.

Sakthivel.K said: (Jan 4, 2017)  
Correct explanations thank you all.

Prasad.P said: (Feb 13, 2017)  
Thanks for solving this sum. It is very helpful to me.

Dilbag said: (Apr 11, 2017)  
Superb explanations. Thank you all.

Suman said: (Jun 7, 2017)  
Thank you all for the given solution.

Nkc said: (Jun 12, 2017)  
In this question, we need a length that can measure all the lenths but the length of the required scale is shortest that can esasily multiples of the given lengths.

Vrinda said: (Jun 28, 2017)  
Why should we add not multiply?

Manasbh said: (Jul 25, 2017)  
Thanks a lot.

Archit said: (Aug 28, 2017)  
It is very simple.

Just check the options , if any option is not divisible by any length then you can rule out that option.

Suppose 15 =3*5 where 3 is not divisible by 700 so it's not the right option.
Now 25 is not divisible by 385 so it is also ruled out,
Now 35 =7*5 which can be divided by all,
And last 42 (is even will give even multiple) which is also not divisible by 385 and you don't even have to check for the last one.

Bunny said: (Feb 13, 2018)  
How to find factors? Someone explain me.

Abhishek said: (Jul 18, 2018)  
Thanks all for explaining the answer.

Prasanth V said: (Aug 11, 2018)  
Thank you @Nareshbora.

Shivi said: (Aug 17, 2018)  
Thanks @Sindhuroyal.

Jaival said: (Aug 20, 2018)  
Thank you for giving the answer.

Sanjeev said: (Sep 12, 2018)  
Why did you consider 385 and 700 only?

Sanjay said: (Jul 29, 2019)  
Can anyone explain me clearly to get it?

Baljit Kaur said: (Apr 24, 2020)  
Thanks All for explaining the problem.

Aarav Barnwal said: (Jul 21, 2020)  
Thank you @Raviteja.

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