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

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

The question is about HCF and LCM. This question is definitely too tough for CAT, but is a wonderful question to conquer that fear of the unknown (x). A range of CAT questions can be asked based on the concept of HCF and LCM. HCF and LCM from CAT Number Systems is oft tested not just in the context of CAT Number Systems but also inside CAT Quantitative Aptitude questions from other topics.

Question 3: There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c. (The answer can be "This cannot be determined").

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2020Online Batches Available Now!

##### Method of solving this CAT Question from Number Theory - HCF and LCM: It is vital not to be intimidated by questions that have a lot of variables in them.

a is a multiple of l and n. Also HCF (l,n) =1; => a has to be a multiple of ln, similarly b has to be a multiple of lm and c has to be a multiple of mn.

We can assume, a = lnx, b = lmy, c = mnz.
Now given that HCF(a, b) = l, that means HCF(nx, my) = 1. This implies HCF(x, y) = 1 and HCF(m, x) = HCF(n, y) = 1.

Similarly it can also be shown that HCF(y, z) = HCF(z, x) = 1 and others also.
So in general it can be written any two of the set {l, m, n, x, y, z} are co-prime.
Now LCM(a, b, c) = LCM (lnx, lmy, mnz) = lmnxyz = abc/lmn.

Quiet obviously, it is a reasonable assumption that a question in CAT will not be as tough as the last one here. However, it is a good question to get an idea of the properties of LCM and HCF.

The question is "Find LCM of a, b, c."

##### Hence the answer is "Cannot be determined"

Quiet obviously, it is a reasonable assumption that a question in CAT will not be as tough as the last one here. However, it is a good question to get an idea of the properties of LCM and HCF.

###### CAT Coaching in ChennaiCAT 2020Enroll at 35,000/-

Online Classroom Batches Starting Now!

###### Best CAT Coaching in ChennaiRegister Online, get Rs 7000/- off

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