# 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.24)

24.

Which of the following fraction is the largest ?

[A].
 7 8
[B].
 13 16
[C].
 31 40
[D].
 63 80

Explanation:

L.C.M. of 8, 16, 40 and 80 = 80.

 7 = 70 ; 13 = 65 ; 31 = 62 8 80 16 80 40 80

 Since, 70 > 65 > 63 > 62 , so 7 > 13 > 63 > 31 80 80 80 80 8 16 80 40

 So, 7 is the largest. 8

 Vijaya said: (Nov 9, 2010) Easy way is 7/8=0.875 13/16=0.8125 31/40=0.775 63/80=0.7875 by this we can easily say dat 7/8 is the largest fraction of them.

 Prashant Pandey said: (Feb 1, 2011) Yes vidya is right.

 Nizamuddin said: (Feb 7, 2011) No Prashant. Vidya is not correct to find the answer. Because you have to calculate all the possible values to retreive the answer. This is long process too rather than the problem explained in the beginning.

 Keerthana said: (Feb 19, 2011) What is explained in the problem is correct.

 Hamsa said: (Feb 22, 2011) How LCM value of 4, 16, 40 and 80 = 80 ?

 Praveen said: (Mar 16, 2011) Its right.

 Jyoti Mehta said: (May 29, 2011) Why we multiply 7/8 to 10 ,13/16 to 5 and 31/40 to 2 ?

 Power Star Pawan Kalyan said: (Jun 6, 2011) @Jyoti Mehta We first find the lcm of the given numbers...7/8,13/16,31/40,63/80 then We'll get that value=80 So.. there goes the process and you'll get the above result...;)

 Rohit said: (Jun 14, 2011) The enswer explained is corect and a time saver too.

 Ashok said: (Aug 7, 2011) This logic is easy to find the answer & time saving too.

 Sandeep Ch said: (Aug 13, 2011) Please explain clearly.

 Folake said: (Sep 8, 2011) Kalyan please explain it very well. I don't really understand that logic.

 Archana said: (Sep 11, 2011) How LCM value of 4, 16, 40 and 80 = 80 ?

 Deepika said: (Sep 17, 2011) @Archana 4,16,40,80 its simple yar first we have to check that 80 have multiples of 4,16,40 like 4*20,16*5,40*2,80*1. So 80 is the correct lcm value check like this is is the easy way.

 Deepika said: (Sep 17, 2011) Hi Vijaya nice short cut.

 Ishan said: (Mar 1, 2012) Deepika you are right.

 Hanumanth said: (Dec 15, 2012) The simple way to solve this type of problems is. The difference between the numerator and denominator less than any of the given numbers is the largest value. Ex: 7/8=1. 13/16=3. 31/40=9. 63/80=17. Less difference is 1 so 7/8 is greater value.

 Naveenkk said: (Feb 1, 2014) Add 1 in for all the numerators. Or simply find the diff bw denominator-numerator whose diff is less that is your answer.

 Yamini.P said: (Apr 14, 2014) First compare the options from this multiply a&b. Cross multiplication, 7/8x13/16 = 112,104, So here 112 is highest so, 7/8 is highest. Again comparison a&c. 7/8x31/40 = 280,240. So here 280 is higher so, 7/8 is highest. Again comparison a&d. 7/8x63/80 = 560,504. So here 560 is higher so, 7/8 is highest. The answer is 7/8 is the higher.

 Shyam said: (May 6, 2014) Dear @Naveenkk can you please explain with details as @Hanumanth. And is this method applicable to all this type of problems. Like those don't have common divisor.

 Viswa said: (Aug 5, 2014) Its wrong lcm of 8,16,40,80 = 160 not 80.

 Sowmya said: (Sep 21, 2014) I think answer given by @Hanumanth is right and easy. But is it applicable to all problems ?

 Dhanya said: (Oct 18, 2014) LCMof 8, 16, 40, 80 is 80 only. It is correct.

 Manju said: (Oct 20, 2014) Hai guys! The following fractions are 7/8, 13/16, 31/40, 63/80. If we take 7/8. First we have to sub these (8-7 =1 ) and divide numerator with 1 (7/1 = 7) same process. 13/16, 16-13 = 3 13/3 = 4.3. 31/40, 40-31 = 9 31/9 = 3.4. 63/80, 80-63 = 17 60/17 = 3.94. By this we can easily say that 7, 4.3, 3.94, 3.4. (this process we can applicable for descending and ascending order).

 Glory said: (Oct 28, 2014) Hi guys, Which one is correct in simple way am confused with your solutions, I need to understand how to use L.C.M in solving that question?

 Amita said: (Nov 13, 2014) (a) 7/8 (b) 13/16 (c) 31/40 (d) 63/80. First of all I compare b/t a and b with cross multiplication. 7/8, 13/16. 7*16 13*8. 112 >104. So 7/8>13/16. Again compare b/t 7/8 and 31/40. 7*40 31*8. 280 > 248, so 7/8>31/40. Again compare b/t 7/8 and 63/80. 7*80 8*63. 560 > 504, so 7/8>63/80. So 7/8 is largest.

 Deepti said: (Nov 27, 2014) The answer given by @Hanumanth is not applicable to all kinds of questions with same nature. I have tried. Its wrong.

 Md. Khurshid said: (Jan 25, 2015) I think @Hanumanth is right, because it is easiest way to check the correct answer that which fraction is larger or smaller.

 Rakesh said: (Mar 10, 2015) 7/8=70/80, 13/16=65/80, 31/40=62/80 this answer how to come?

 Asif said: (Apr 30, 2015) I think @Vijaya is right, because it is easiest to check the correct answer that which fraction is larger or smaller.

 Sikha said: (Jul 25, 2015) I don't understand how we are getting 7/8 = 70/80. 13/16=65/80. 31/40=62/80. Please somebody explain me dis?

 Arts Ashokan said: (Sep 13, 2015) (7/8)*10 = 70/80; (13/16)*5 = 65/80; (31/40)*2 = 62/80;

 Manik Sharma said: (Oct 15, 2015) I don't understand how 7/8 = 70/80?

 Pritam said: (Nov 17, 2015) How the LCM will be 80?

 Tasik said: (Jan 4, 2016) @Manju. It's not 60/9. It's 63/9 = 7 (It also get 7). Then which is largest?

 Kanhaiya said: (Mar 30, 2016) How we get it?

 Sarah said: (May 13, 2016) LCM of 8, 16, 40 and 80 is 80 then, 80/8 = 10. 80/16 = 5. 80/40 = 2. 80/80 = 1 then, 7/8 * 10/10 = 70/80. 13/16 * 5/5 = 65/80. 31/40 * 2/2 = 62/80. 63/80 * 1 = 63/80. 70/80 > 65/80 >63/80 > 62/80. So 7/8 is largest.

 Angilina Jolie said: (Aug 17, 2016) Thank you so much @Sarah.

 Naveen said: (Dec 28, 2016) You are correct @Sarah.

 Vaibhav said: (Apr 14, 2017) Hello, guys. The lcm is 80. So we have to make 80 as the base for all numbers. In this example, if we want to make base 80 for no 7/8 we have to multiply the N and D by 10. For 13/16 for base 80-multiply N and D by 5. For 31/40 for making base 80 multiply N and D by 2. And 4rth no already has base 80 so we don't need anything to do.

 Sruthi said: (May 27, 2017) Well said @Vaibhav and @Hanumanth.

 Sharath.S said: (Jul 1, 2017) Perfect explanation, thanks @Sarah.

 Khagendra said: (Oct 16, 2017) Awesome shortcut, thanks @Sarah.

 Vishwanath said: (Sep 21, 2018) Since there denominators are divisible by 8, simplify them into. 7/1, 13/2, 31/5, 63/10. After solving them, it's clear that 7 is the largest.

 Kriti said: (Oct 5, 2018) As per my knowledge, the fraction whose denominator is the smallest is the largest fraction.

 Ajkniu said: (Aug 28, 2019) As per my knowledge, the fraction whose denominator is the smallest is the largest fraction.

 Saumyojit Das said: (Oct 20, 2019) Why we are taking out LCM why not HCF? HCF will also give a common factor in the denominator.