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

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 24)
24.
Which of the following fraction is the largest ?
 7 8
 13 16
 31 40
 63 80
Answer: Option
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

Discussion:
49 comments Page 1 of 5.

Mayur said:   3 years ago
First find LCM Of denominator;
LCM of 8,16,40,80=80

Now let's same all the denominator
7*10/8*10. = 70/80.
13*5/16*5. = 65/80.
31*2/40*2 62/80.
63*1/80*1. 63/80.
As u can see all the denominators is the same,
So see numerator now 70/80 { 70 is biggest}

Which means
7/8 Is the largest fraction.
(9)

Sirin said:   3 years ago
Lcm is

8 16 40 80.

Factor is 2 * 2 * 2 * 5 * 2 = 80.

Saumyojit Das said:   5 years ago
Why we are taking out LCM why not HCF?

HCF will also give a common factor in the denominator.

Ajkniu said:   5 years ago
As per my knowledge, the fraction whose denominator is the smallest is the largest fraction.
(1)

Kriti said:   6 years ago
As per my knowledge, the fraction whose denominator is the smallest is the largest fraction.
(4)

Vishwanath said:   6 years ago
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.
(2)

Khagendra said:   7 years ago
Awesome shortcut, thanks @Sarah.
(1)

Sharath.s said:   7 years ago
Perfect explanation, thanks @Sarah.

Sruthi said:   7 years ago
Well said @Vaibhav and @Hanumanth.

Vaibhav said:   7 years ago
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.
(2)

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