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CAT Number System, HCF & LCM Questions, LR & DI | Day 6 Preparation for CAT 2025
HCF and LCM are key topics in the CAT Quantitative Ability section, forming a significant and frequently tested part of the Number System syllabus. These concepts require a thorough understanding, strategic practice, and quick problem-solving skills to excel. As part of the Day 6 preparation strategy for CAT 2025, this article focuses on effective methods and shortcuts to master HCF and LCM questions, helping aspirants strengthen their fundamentals, boost accuracy, and improve overall speed for a higher CAT score. Consistent practice and conceptual clarity in these areas can greatly enhance your performance in the exam.
Part-1: Quantitative Aptitude for CAT 2024
Topic: Number System questions for CAT (HCF and LCM CAT questions) Highest Common Factor (HCF and LCM / GCD):
HCF is the highest common divisor which divides two (or more) numbers completely.
For Example,
12 is HCF of 36 and 48.
17 is HCF of 340 and 357
3 x 22 is LCM of (3x 24 and 33 x 22)
The most common ways of finding HCF are
Prime Factorization Method:
Eg: To find HCF of 27 and 36
27 = 33
36 = 22 x 32
HCF = 32
Division Method:
Eg: To find HCF of 27 and 36
Divide 36 by 27; the remainder is 9
Divide 27 by 9; the remainder is 0.
(This process is repeated till the remainder is 0)
Least Common Multiple (LCM):
The least value which is divisible by two or more values completely, is LCM.
For Example:
72 is LCM of 8 and 9.
2184 is LCM of 8, 13 and 21.
33 x 24 is LCM of (3x 24 and 33 x 22)
The most common way of finding LCM is
Prime Factorization Method:
Eg: To find LCM of 27 and 36
27 = 33
36 = 22 x 32
LCM = 22 x 33
HCF and LCM questions, CAT Number System Questions From CAT Previous Year Papers/ HCF and LCM questions for CAT exam
The two previous year CAT questions on number system (HCF and LCM)are given below:
Q1. How many pairs of positive integers x, y exist such that HCF of x, y = 18 and product of x and y = 1620? [ CAT Question Paper]
2
8
1
3
Solution: C
Let the two numbers be 18a and 18b where a and b are co-prime numbers.
Also, 18a x 18b = 1620
So, a x b = 1620/ (18 x 18) = 5
Therefore, (a, b) = (1, 5); the only possible pair in a and b.
Q2. A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour? [CAT Question Paper ]
30
24
20
60
Solution: A
Red light flashes after every 60/3=20 sec
Green light flashes after every 120/5=24 sec
Both lights will flash together if the multiples of flushing times are common
i.e. LCM (20,24) =120 sec = 2min
Thus, both lights will flash together at intervals of 120 sec= 2 minute
In 1 hour, both lights flash together 60/2 = 30 times.
Prerequisite:
To prepare for the number system for CAT exam, students must have knowledge of:
Prime, composite, and Co-primes
Factors
Multiples
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Use NowTips On CAT Preparation For Number System (HCF and LCM ):
The smallest number which when divided by a, b and c leaves a remainder R in each case then the number will be (L.C.M of a, b, c) + R.
The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)
The greatest number which divide x, y, z to leave remainders a, b, c respectively is
H.C.F of (x – a), (y – b) and (z – c)
LCM of (a/b, c/d, e/f) = LCM (a, c, e)/ HCF (b, d, f)
HCF of (a/b, c/d, e/f) = HCF (a, c, e)/ LCM (b, d, f)
Practise different kinds of problems.
HCF of a and b × LCM of a and b = a × b
Apply the concepts to practise HCF and LCM questions.
Practise previous year CAT questions on number systems and LCM and HCF problems.
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References to Study (Theory):
Learn the concept of HCF and LCM from class 10 Mathematics NCERT (For Theory)
Arun Sharma: A Quantitative Approach for CAT (6th Edition)
2iim Online Learning Classroom
References to Study (Practice):
MASTER Number System for CAT and GMAT by Nishit K Sinha.
Sample Papers
CAT previous year papers
Part-2: Logical Reasoning and Data Interpretation
Topic: Data Interpretation (Spider/ Radar Graph)
In previous articles-Day 5, strategies for DI based on Bar graph, Pie chart, Table graph and Line graph have been discussed. A different kind of DI on spiders will be discussed in this article for the CAT exam. Data interpretation is a must-come topic in the CAT Exam and other management entrance exams.
DI on Spider (Radar) Graph
It consists of equiangular spokes and each spoke represents one variable. These charts contain 0 at its centre.
This is a spider chart for 5 variables.
A=70
B=58
C=5
D=15
E=25
Blue line shows the value of a commodity on 5 different parameters.
Questions Based On Spider Graph From CAT Previous Year Papers
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability.
Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cost. [CAT Question Paper 2019- slot 1]
Q1. On which aspect is the median score of the five vendors the least?
Customer Service
Cost
Reliability
Quality
Ans: (1)
The median is the mid-value. For all six parameters median is as follows:
Reliability=52-53
Reach=65
Quality=62
Features=55
Customer Service = 50 (least)
Cost =75
Q2. A vendor's final score is the average of their scores on all six aspects. Which vendor has the highest final score?
Vendor 1
Vendor 2
Vendor 3
Vendor 4
Ans: (2)
Total Score of Vendors:
Vendor 1 = (52+ 80+ 73+ 40 + 55 + 75) = 375
Vendor 2 = (40+ 58+ 70+ 45 + 42 + 80) = 335
Vendor 3 = (75+ 66+ 60+ 50+ 55+ 90) = 396
Vendor 4 = (25+ 45+ 40+ 90+ 70+ 70) = 340
Vendor 3 has the highest total and hence the highest average.
Q3. A list of all the vendors who are among the top three vendors on all six aspects is?
None of the Vendors
Vendor 1
Vendor 3
Vendor 1 and Vendor 3
Ans: (3)
Vendors in top 3 in each aspect:
Reliability = Vendor 3, Vendor 5 and Vendor 1
Reach = Vendor 1, Vendor 5, Vendor 3
Quality = Vendor 1, Vendor 2, Vendor 3
Features= Vendor 4, Vendor 5, Vendor 3
Customer Service = Vendor 4, Vendor 1, Vendor 3
Cost = Vendor 3, Vendor 2, Vendor 1
Clearly only vendor 3 appears in all the three.
Prerequisite:
To Prepare Data Interpretation (Spider graph) for the CAT 2024, a student must learn:
Percentage (Basic)
Simplification and approximation
Mean, Mode and Median
Observational Skills
References to Study (Theory):
LRDI for CAT and GMAT by Nishit K Sinha.
Crack XAT YouTube Channel
References to Study (Practice):
https://online.2iim.com
How to Prepare for Data Interpretation for CAT by Arun Sharma
CAT previous year papers
Part-3: VARCTopic: Articles And Its Uses
Article is one of the parts of speech in English grammar which is used to modify the Noun entities.
Indefinite Articles (A and An): Used with singular nouns only.
Examples:
An honest man.
A tall man.
Tomorrow a man will come to see you.
Definite Article (The): Refers to specific nouns and can be used with both singular and plural nouns.
Examples:
The man on dice is my ideal.
The Bible.
Practice Questions On Articles
Direction: Choose the correct article
Q.1 Who is _________ of England now.
the prime minister
a prime minister
Ans: A
Q2. There is _________ restaurant near my house.
a nice
nice
- Ans: A
Q3. My grandparents live in _____________ of the city
south
the south
Ans: B
Q4. Is this _____________ Australian breed?
a
an
Ans: B
Prerequisite:
Knowledge of Verbal sound.
Knowledge of Noun (singular and Plural)
CAT Preparation Tips To Prepare Articles And Its Uses
Articles do not use uncountable nouns.
Learn the specific cases where articles should not be used
Ex: Let’s go out for dinner tonight. (Incorrect)
Let’s go out for dinner tonight. (Correct)
Articles should not be used with pronouns.
Use no Article before names of sports, subjects, nationalities, and languages.
Develop reading habits.
Practice more and more exercises.
References to Study (Theory):
Advanced English grammar by Wren and Martin (Oxford)
engvid.com (YouTube channel as well as Web)
References to Study (Practice):
Questions bank from iquanta.com
Oxford Practice Grammar (sixth edition)
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
HCF LCM Question Weightage for CAT Exam
The HCF and LCM topic consistently appears in the CAT exam, with around 2 questions each year from 2020 to 2024. Mastering these concepts is crucial for scoring well in the Quantitative Aptitude section and improving overall performance and CAT marks.
Year | Topic Name | Number of Questions |
2020 | HCF and LCM | 2 |
2022 | HCF and LCM | 2 |
2023 | HCF and LCM | 2 |
2024 | HCF and LCM | 2 |
Short Tricks to Crack LCM HCF Questions for CAT 2025
LCM and HCF questions are quick to solve once you master a few smart tricks. These concepts are based on number properties and often appear in the CAT Quantitative Aptitude section. Use the shortcuts below to solve such questions faster and with greater accuracy.
1. Prime Factorisation Method
Trick:
Break numbers into their prime factors.
LCM = Product of the highest powers of all primes
HCF = Product of lowest powers of common primes
Example:
Find LCM and HCF of 12 and 18.
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 36
HCF = 2 × 3 = 6
2. Product Rule
Trick:
For two numbers:
LCM × HCF = Product of the numbers
Example:
Find LCM if HCF of 8 and 32 is 8.
Product = 8 × 32 = 256
LCM = 256 ÷ 8 = 32
3. Co-Prime Shortcut
Trick:
If two numbers are co-prime (HCF = 1),
LCM = Product of the numbers
Example:
Find LCM of 5 and 12
Since HCF(5,12) = 1 → LCM = 5 × 12 = 60
4. Euclidean Algorithm for HCF
Trick:
Use repeated division
HCF(a, b) = HCF(b, a % b)
Example:
Find the HCF of 48 and 18
48 % 18 = 12
18 % 12 = 6
12 % 6 = 0 → HCF = 6
5. HCF and LCM of Fractions
Trick:
HCF of fractions = HCF of numerators / LCM of denominators
LCM of fractions = LCM of numerators / HCF of denominators
Example:
Find HCF of 2/5 and 4/15
HCF(2, 4) = 2
LCM(5, 15) = 15
HCF = 2 / 15
6. Work Backwards Using Product Rule
Trick:
If LCM or HCF is given, use options and check if:
LCM × HCF = Product of numbers
Example:
If HCF = 4 and LCM = 60, find the pair.
Check options like (12, 20): 12 × 20 = 240;
LCM × HCF = 60 × 4 = 240
We will be back with Day-7 strategy tomorrow at the same time. keep practising and be focused. Students can practice number system mock test for CAT and can also practice DILR and VARC alongside as well.
Frequently Asked Questions (FAQs)
Q: How can I practice HCF and LCM questions effectively for CAT?
A:
Solve previous years’ questions, use online quizzes, and apply shortcuts regularly. Focus on understanding concepts deeply and practising mixed problem sets for better performance.
Q: How important is the HCF and LCM topic for CAT 2025?
A:
HCF and LCM consistently appear in CAT with 2 questions yearly. Mastering this topic helps solve problems quickly, boosting your score in the Quantitative Aptitude section.
Q: What are the best methods to solve HCF and LCM questions efficiently?
A:
Use prime factorisation, the product rule (LCM × HCF = product), and the Euclidean algorithm for quick calculations. Practice regularly to improve speed and accuracy.
Q: How many questions on average are asked about HCF and LCM in CAT exams?
A:
On average, CAT features 2 questions from HCF and LCM each year, making it a reliable scoring topic for candidates who prepare well.
Q: Can HCF and LCM questions be tricky, or are they mostly straightforward?
A:
Most HCF and LCM questions are simple but can be combined with other concepts like ratios or time-speed-distance, requiring careful analysis and practice.
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Have a question related to CAT ?
HELLO,
With a 74 percentile in CAT ,EWS category and 8/8/7 academics , you are in good spot for many non IIM colleges like :-
1.BIMTECH
2.AIM DELHI
3.AMITY GROUP
4.IMT
5.IMT NAGPUR
6.SDM IMD
7.Great Lakes (GLIM) Institute of Management
8.Alliance University
9.IBS Business School
10. Institute of Management,
Hello there,
Yes, you should surely give a try. Your score and being Non-Engineer gives you an edge. The previous trends shows that cutoff typically hovers around 75-84 for EWS category. Therefore you must give a try.
NIBM gives proper weightage to academics as well, therefore your 8\8\8 would work
HELLO,
With an overall 98.54 percentile ( QA/DILR 97.55, VARC 94.89) and strong academics 9/9/0, you have a good profile. As a B.Tech candidate you can expect calls from :-
- IIM Shillong
- IIM Udaipur
- IIM Trichy
- IIM Ranchi
- IIM Raipur
- IIM Kashipur
- IIM Nagpur
- IIM Indore is Boderline
Hope this
Hello there,
The IIMs you should expect are listed below:
- A 90-100% chance: IIM Lucknow, IIM Indore, IIM Kozhikode, IIM Shillong, IIM Mumbai, and all CAP IIMs( Udaipur, Trichy, Ranchi, etc.).
- A 50-70% CHANCE: IIM Calcutta and SPJIMR.
- A very competitive chance, IIM Ahmedabad and IIM Bangalore
Your biotech background
Hello there,
With a 70 percentile it is not easy to make it in the IMT Hyderabad because the cutoff usually reaches 85-90+ for general category, even IMT Nagpur has low chances since the cutoff usually reaches 75-85. However, IMI Kolkata, is your safe option, since the cutoff is around
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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