# CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

###### CAT Questions | Number Theory | HCF and LCM

The question is about HCF and LCM. We need to find all the possible pairs of (x,y), given the product of them and their HCF. Dealing with HCF and LCM of numbers is a vital component in CAT Number Theory: HCF and LCM. A range of CAT questions can be asked based on this simple concept. In CAT Exam, one can generally expect to get 1~2 questions from CAT Number Systems: HCF and LCM. In multiple places, extension of HCF and LCM concepts are tested by CAT Exam and one needs to understand HCF and LCM to be able to answer the same. CAT Number theory is an important topic with lots of weightage in the CAT Exam.

Question 1: How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?

1. 8
2. 7
3. 9
4. 12

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

##### Method of solving this CAT Question from Number Theory - HCF and LCM: Given two numbers, finding HCF, LCM is very easy. Given some property about HCF and the numbers, finding the numbers is much tougher.

We need to find ordered pairs (x, y) such that xy * HCF(x, y) = 1080.
Let x = ha and y = hb where h = HCF(x, y) => HCF(a, b) = 1.
So h3(ab) = 1080 = (23)(33)(5).
We need to write 1080 as a product of a perfect cube and another number.

Four cases:
1. h = 1, ab = 1080 and b are co-prime. We gave 4 pairs of 8 ordered pairs (1, 1080), (8, 135), (27, 40) and (5, 216). (Essentially we are finding co-prime a,b such that a*b = 1080).

2. h = 2, We need to find number of ways of writing (33) * (5) as a product of two co-prime numbers. This can be done in two ways - 1 and (33) * (5) , (33) and (5)
number of pairs = 2, number of ordered pairs = 4

3. h = 3, number of pairs = 2, number of ordered pairs = 4

4. h = 6, number of pairs = 1, number of ordered pairs = 2

Hence total pairs of (x, y) = 9, total number of ordered pairs = 18.
The pairs are (1, 1080), (8, 135), (27, 40), (5, 216), (2, 270), (10, 54), (3, 120), (24, 15) and (6, 30).

The question is "How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?"

##### Hence the answer is "9"

Choice C is the correct answer.

###### CAT Coaching in ChennaiCAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

###### Best CAT Coaching in Chennai

Attend a Demo Class

## CAT Online Coaching | CAT Number Systems questions Videos On YouTube

#### Other useful sources for Number System Questions | Number Theory HCF and LCM Sample Questions

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com