30+ CAT HCF and LCM Questions with Answers & Short Solutions (Free PDF)

Looking for HCF LCM CAT Questions to practice for CAT 2026? This set includes 30+ exam-style questions from Number System remainders, divisibility, cyclic patterns, and word problems along with answers, quick methods, and a free PDF for timed practice.

Some questions are based on the concepts and patterns seen in the CAT 2025 question paper. These can help you understand how HCF and LCM are asked in CAT and prepare better for CAT 2026.

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Key Takeaways

• HCF and LCM are important topics in the CAT Number System.
• Around 2–3 questions are usually seen from these concepts in CAT QA.
• Questions are often based on remainders, divisibility, and number patterns, rather than direct formula-based questions.
• Strong fundamentals can help you solve questions in under a minute
• Frequently used in word problems and real-life scenarios

What You Will Get in This Blog: You will get 30+ important HCF and LCM CAT questions with answers, along with key concepts, solving techniques, and practice strategies to help you improve speed, accuracy, and confidence for CAT 2026.

What are HCF LCM CAT Questions? 

CAT HCF and LCM questions are a type of problem from the Number System topic in the Quantitative Aptitude section of the CAT Exam.

They require applying the concepts of Highest Common Factor (HCF) and Least Common Multiple (LCM), often in complex or application-based scenarios, rather than simple, direct calculations.

The HCF LCM CAT questions test not only the definitions of HCF and LCM but also their properties and applications in various word problems.

Download HCF–LCM CAT Questions PDF (Answers + Solutions)

30+ Most Important HCF LCM CAT Questions with Answers

To help you out, we have provided 30+ important HCF LCM CAT Questions 2026. Practice them to boost your CAT 2026 Preparation:

Que 1: How many pairs of positive integers (x,y) exist such that HCF(x,y) + LCM (x,y)=91? 

1. 6 
2. 7 
3. 8 
4. 10

Correct Answer: 8

Que 2: The LCM of two natural numbers p and q where p>q is 935. What is the maximum possible sum of the digits of q? 

1. 1 
2. 8 
3. 16 
4. 2

Correct Answer: 16

Que 3: The HCF of two numbers is 12 and their product is 31104. How many pairs of such numbers are possible? 

1. 1 
2. 2 
3. 3 
4. 4

Correct Answer: 2

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Que 4: Let a and b be two positive integers such that their LCM is 300. How many ordered pairs (a,b) are possible? 

1. 38 
2. 39 
3. 75 
4. 76

Correct Answer: 76

Que 5: Find the smallest number that leaves a remainder of 4 on division by 5, a remainder of 5 on division by 6, a remainder of 6 on division by 7, a remainder of 7 on division by 8, and a remainder of 8 on division by 9. 

1. 2519 
2. 5039 
3. 1079 
4. 979

Correct Answer: 2519

Que 6: A number, when divided by 3,4,5, and 6, always leaves a remainder of 2, but leaves no remainder when divided by 7. What is the lowest such number possible? 

1. 122 
2. 182 
3. 242
4. 302

Correct Answer: 182

Que 7: The greatest number which on dividing 1665 and 2037 leaves remainders 6 and 5 respectively is:

1. 123 
2. 127 
3. 235 
4. 305

Correct Answer: 127

Que 8: A room is 4 meters 37 cm long and 3 meters 23 cm broad. The floor needs to be paved with a minimum number of square slabs. Find the least number of slabs required for this purpose. 

1. 485
2. 431 
3. 391 
4. 381

Correct Answer: 391

Que 9: The traffic lights at three different road crossings change after every 24 sec., 36 sec., and 72 sec. respectively. If they all change simultaneously at 8:20:00 hrs, when will they again change simultaneously? 

1. 8:21:12 hrs 
2. 8:28:22 hrs 
3. 8:27:36 hrs 
4. 8:27:48 hrs

Correct Answer: 8:21:12 hrs

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Que 10: 24 mango trees, 56 apple trees and 72 orange trees have to be planted in rows such that each row contains the same number of trees of one variety only. What is the minimum number of rows required to plant all the trees? 

1. 12 
2. 16 
3. 19 
4. 24

Correct Answer:19

Que 11: How many natural numbers divide exactly one out of 1080 and 1800, but not both? 

1. 20 
2. 42 
3. 24 
4. 36

Correct Answer: 20

Que 12: A natural number n is such that 120≤n≤240. If HCF(n,240)=1, how many values of n are possible? 

1. 24 
2. 32 
3. 36 
4. 40

Correct Answer: 32 

Que 13: Find the HCF of 220−1 and 230−1. 

1. 25−1 
2. 210−1 
3. 220−1 
4. 250−1

Correct Answer: 210−1

Que 14: The HCF of two expressions is (x+3) and their LCM is (x3+9x2+23x+15). If one expression is (x2+8x+15), find the other expression. 

1. x2+4x+3 
2. x2+3x+3 
3. x2+6x+5 
4. x2+7x+12

Correct Answer: x2+4x+3

Que 15: The sum of two numbers is 1050. What is the maximum possible value of the HCF between the two numbers? 

1. 350 
2. 700 
3. 1050 
4. 525

Correct Answer: 525

Que 16: The HCF of two numbers is 35 and their sum is 1085. How many pairs of such numbers are possible? 

1. 12 
2. 15 
3. 18 
4. 30

Correct Answer: 15 

Que 17: Find the smallest number which when divided by 18,24,30 and 42 leaves a remainder of 5,11,17 and 29, respectively. 

1. 2513 
2. 2501 
3. 2520 
4. 2507

Correct Answer: 2507

Que 18: Find the least multiple of 13 which on dividing by 4,5,6,7, and 8 leaves a remainder of 3 in each case. 

1. 843 
2. 2523 
3. 1683 
4. 1263

Correct Answer: 2523

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Que 19: Three runners A,B, and C start running from the same point on a circular track of 1200 meters at the same time and in the same direction. Their speeds are 4 m/sec, 6 m/sec, and 10 m/sec respectively. After how much time will they meet again at the starting point for the first time? 

1. 10 minutes 
2. 15 minutes 
3. 20 minutes 
4. 1 hour

Correct Answer: 10 minutes

Que 20: A merchant has three different types of oil: 324 litres, 351 litres, and 459 litres. Find the minimum number of casks of equal size required to store the oil without mixing. 

1. 42 
2. 45 
3. 51 
4. 61

Correct Answer: 42

Que 21: Find the LCM of the fractions 32,94,65. 

1. 310 
2. 2720 
3. 320 
4. 910

Correct Answer: 320

Que 22: The LCM of two numbers is 210 and their HCF is 7. The two numbers are in the ratio 2:3. Find the sum of the two numbers. 

1. 49 
2. 70 
3. 35 
4. 63

Correct Answer: 49 

Que 23: The number of common terms in the two sequences: 15,19,23,27,…,415 and 14,19,24,29,…,464 is: 

1. 19 
2. 20 
3. 21 
4. 22

Correct Answer: 20

Que 24: How many ordered triplets (a,b,c) of positive integers exist such that LCM(a,b)=1000, LCM(b,c)=2000, LCM(c,a)=2000? 

1. 20 
2. 24 
3. 28 
4. 32

Correct Answer: 28 

Que 25: The least common multiple of a number N and 990 is 6930. The greatest common divisor of N and 550 is 110. What is the sum of all possible values of N? 

1. 7700 
2. 10010 
3. 7920 
4. 7040

Correct Answer: 7700 

Que 26: For how many ordered pairs (a,b) of natural numbers is the LCM of a and b equal to 23×34? 

1. 36 
2. 45 
3. 54 
4. 63

Correct Answer: 63

Que 27: The product of two positive integers x and y is 1080. If HCF(x,y)=h, how many distinct values can h take? 

1. 8 
2. 9 
3. 10 
4. 12

Correct Answer: 9

Que 28: How many pairs of integers (x,y) exist such that the product of x, y, and HCF(x,y) is 1080? (Assume x,y are positive integers). 

1. 9 
2. 12 
3. 18 
4. 27

Correct Answer: 12

Que 29: Four bells ring at intervals of 6 sec, 12 sec, 15 sec, and 20 sec respectively. If they all start ringing together, how many times will they toll together in 2 hours? 

1. 120 
2. 121 
3. 122 
4. 123

Correct Answer: 121 

Que 30: Four logs of wood of lengths 541 m, 11513 m, 321 m, and 4109 m are cut into small pieces, all of which have equal length. Each piece of wood is as lengthy as possible. Each cut piece is given to a set of 2 carpenters to work on. How many carpenters are there in all to work? 

1. 266 
2. 148 
3. 210 
4. 332

Correct Answer: 266 

Find: Important Formulas for CAT 2026 

Que 31: Find the least number which when divided by 2,3,4,5,6 and 7 leaves no remainder, and which is also the largest number less than 1800 satisfying this condition. 

1. 1260 
2. 1680 
3. 1750 
4. 1800

Correct Answer:1680 

Que 32: The HCF of two numbers A and B is 12. If A and B are greater than 12 and their product is 864, find the difference between the two numbers. 

1. 12
2. 24 
3. 36 
4. 48

Correct Answer: 48

Tips to Prepare for CAT HCF and LCM Questions 2026

HCF and LCM are part of the Number System topics covered in the CAT Syllabus. Start with the basic concepts and then move to questions based on remainders, divisibility, and co-prime numbers. Regular practice will help you solve these questions faster.

• Clear the basics: First understand what HCF and LCM mean and how they are used in divisibility questions.
• Practise both methods: Learn the torisati division methods for finding HCF and LCM.
• Work on word problems: Practise questions involving remainders, divisibility, and finding the smallest or greatest possible number.
• Know co-prime numbers: If two numbers are co-prime, their HCF is 1, and their LCM is the product of the two numbers.
• Try different types of numbers: Practise with integers as well as fractions to get comfortable with different question patterns.
• Solve CAT PYQs: Go through CAT Previous Year Papers to see how HCF and LCM are asked in the exam.
• Practise with a timer: Once your concepts are clear, solve HCF LCM CAT Questions within a set time to improve your speed.
• Check your mistakes: Go back to questions you got wrong, especially those based on remainders and co-prime numbers.
• Revise every week: Keep some time for regular revision so that the formulas and methods
• stay fresh.

Conclusion

HCF and LCM questions are usually easy to understand, but the way they are framed in CAT can sometimes make them tricky. Learning the basic methods well can also help you save time in other Number System questions.

HCF and LCM are important topics in the CAT Quantitative Aptitude section and are generally considered manageable with proper practice.

Instead of memorising formulas, focus on understanding the concepts and solving different types of questions. This will make it easier to handle questions based on divisibility, remainders, and multiples.