30+ Most Important HCF LCM CAT Questions with Answers

Overview: Boost your CAT score and percentile with the most important HCF LCM CAT questions. Read on to know about the key prep tips to follow while solving these questions.

The CAT 2026 exam is scheduled on the last Sunday of November, and thus, it is essential to practice as many questions as possible to improve your CAT QA speed and accuracy.

HCF and LCM are the core part of the CAT Number system questions. Each year, around 2-3 questions are asked from this section.

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Therefore, CAT aspirants should be well aware of the types of CAT questions, their difficulty levels, and tips for solving them.

Here, we have provided 30+ most important HCF LCM CAT questions that can help you polish your speed and accuracy. Read on HCF LCM CAT Questions to know more!

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 (Common Admission Test) 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 questions test not only the definitions of HCF and LCM but also their properties and applications in various word problems.

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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

Check Now: Most Frequently Asked CAT QA Questions

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

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

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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 

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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

• Master the Basics First: Understand what HCF (Highest Common Factor) and LCM (Least Common Multiple) mean and how they relate to divisibility and multiples.
• Learn the Two Main Methods: Practice both the Prime Factorisation Method and the Division Method to find HCF and LCM faster.
• Apply HCF–LCM to Word Problems: Focus on types like finding the smallest number leaving specific remainders or the greatest number dividing numbers with given remainders.
• Understand Co-primes: If two numbers are co-prime, their HCF = 1 and LCM = product of the two numbers.
• Focus on Conceptual Variety: Practice with both integer and fractional numbers to strengthen flexibility.
• Solve Previous Year CAT Questions: Go through past CAT papers and sectional tests to identify how number systems integrate HCF–LCM indirectly.
• Time Your Practice: Use timed mocks to improve accuracy and speed. These HCF LCM CAT questions can be solved in under a minute with practice.
• Review Errors: When practising, review mistakes to identify pattern,s especially in remainder and co-prime questions.
• Revise Regularly: Keep short weekly revision sessions to maintain formula recall and improve mental calculation speed.

Click Here: Download CAT Arithmetic questions PDF with Solutions 

Conclusion

CAT HCF and LCM questions are Easy to learn, tricky by design. Mastering them early helps unlock time-saving strategies for more complex problems.

HCF and LCM form a fundamental part of the Number System and are among the easiest scoring topics in the CAT Quantitative Aptitude section.

The key to mastering this topic lies in clarity of concepts, regular practice, and application-based understanding rather than rote memorisation.