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50+ IPMAT HCF and LCM Questions PDF Download with Answers
August 26, 2026
Preparing for IPMAT? This page compiles the most asked HCF & LCM question types direct, ratio-based, remainder-based, and word problems along with shortcuts and common mistakes. Use the solved examples first, then attempt the practice set, and finally download the 50-question PDF for timed revision.
HCF and LCM are two of the most important concepts to understand while preparing for the Number System section for IPMAT.
Questions based on these concepts can be straightforward when asked directly, but they can also involve ratios, remainders, divisibility, and real-life situations that require a little more thinking.
If you are looking for IPMAT HCF and LCM Questions to strengthen your quantitative aptitude preparation, this guide brings together the key formulas, shortcuts, solved examples, and practice problems you need to know.
The aim is not just to help you remember formulas, but to help you identify the right approach quickly when you come across an HCF or LCM problem in the exam.
IPMAT HCF and LCM Questions: Important Formulas
The IPMAT Quantitative section is a scoring section if you solve it accurately, and to do that, you need to know all the important formulas.
Before solving HCF and LCM questions for IPMAT, make sure these formulas are familiar.
| Concept | Formula / Method | Example / Explanation |
|---|---|---|
| Product Relationship | HCF(a, b) × LCM(a, b) = a × b | For two positive integers, this relationship can be used to find the missing value. |
| Find LCM | LCM = (a × b) ÷ HCF | If two numbers and their HCF are known, use this formula to find their LCM. |
| Find HCF | HCF = (a × b) ÷ LCM | This is useful when the LCM and the two numbers are given. |
| Prime Factorisation Method | For HCF, take the smallest powers of common primes. | 24 = 2³ × 3 and 36 = 2² × 3². Therefore, HCF = 2² × 3 = 12. |
| Prime Factorisation for LCM | For LCM, take the highest powers of all primes appearing in the numbers. | 24 = 2³ × 3 and 36 = 2² × 3². Therefore, LCM = 2³ × 3² = 72. |
| Co-Prime Numbers | If two numbers have no common factor other than 1, HCF = 1 and LCM = the product of the numbers. | 7 and 10 are co-prime. Therefore, HCF = 1 and LCM = 70. |
| Numbers in a Given Ratio | If two numbers are in the ratio a:b and their HCF is h, the numbers can be represented as ah and bh. | If two numbers are in the ratio 3:5 and their HCF is 4, the numbers are 12 and 20 |
Download LCM and HCF Problems with Solutions PDF
Here is the complete list of the 50 most important IPMAT HCF and LCM questions with solutions:
IPMAT HCF and LCM Questions 2027 with Solutions
Q1. What is the HCF of any two consecutive even numbers (e.g., 24 and 26)?
a) 1
b) 2
c) 4
d) It varies
Answer: b) 2
Solution: Consecutive even numbers always share exactly the factor 2, since they differ by 2 and both are even.
Q2. Find the LCM of two consecutive numbers, 7 and 8.
a) 15
b) 28
c) 56
d) 112
Answer: c) 56
Solution: Consecutive numbers are always co-prime, so LCM = product = 7×8 = 56.
For more practice, you can also check out the IPMAT Geometry questions and answers for IPMAT 2027.
Q6. 615 boys and 963 girls are to be seated in rows for an exam such that each row has the same number of students and contains only boys or only girls. Find the maximum possible number of students per row.
a) 3
b) 9
c) 15
d) 21
Answer: a) 3
Solution: Maximum students per row = HCF(615, 963) = 3.
Q7. Find the length of the longest tape that can exactly measure 7 m, 3 m 85 cm, and 12 m 95 cm.
a) 5 cm
b) 15 cm
c) 35 cm
d) 55 cm
Answer: c) 35 cm
Solution: Convert to cm: 700, 385, 1295. HCF(700,385,1295) = 35 cm.
Q8. Three numbers are in the ratio 2:3:4 and their LCM is 240. Find the numbers.
a) 20, 30, 40
b) 30, 45, 60
c) 40, 60, 80
d) 60, 90, 120
Answer: c) 40, 60, 80
Solution: Let the numbers be 2x, 3x, 4x. Since these share no common factor, LCM = 12x = 240, so x = 20. Numbers = 40, 60, 80.
Check out the complete IPMAT syllabus for more important topics, subtopics, sectional weightage and more.
Q19. Two numbers are in the ratio 3:4, and their HCF is 4. Find their LCM.
a) 36
b) 42
c) 48
d) 56
Answer: c) 48
Solution: Numbers = 3×4=12 and 4×4=16. LCM(12,16) = 48.
Q9. Two numbers are in the ratio 4:5, and their HCF is 6. Find their LCM.
a) 100
b) 110
c) 120
d) 150
Answer: c) 120
Solution: Numbers = 24 and 30. LCM(24,30) = 120.
Q10. Three bells ring at intervals of 6, 8 and 12 minutes. If they ring together now, after how long will they ring together again?
a) 16 min
b) 20 min
c) 24 min
d) 48 min
Answer: c) 24 min
Solution: LCM(6,8,12) = 24 minutes.
HCF and LCM Practice Questions for IPMAT
Once you have worked through the solved examples, try solving questions without looking at the solution.
Practice Question 1: Find the HCF of 84, 126 and 210.
Answer: 42
Method:
Prime factorisation gives:
84 = 2² × 3 × 7
126 = 2 × 3² × 7
210 = 2 × 3 × 5 × 7
The common prime factors with the lowest powers are:
2 × 3 × 7 = 42
Practice Question 2: Find the LCM of 18, 24 and 40.
Answer: 360
Solving Method:
18 = 2 × 3²
24 = 2³ × 3
40 = 2³ × 5
Take the highest power of every prime:
LCM = 2³ × 3² × 5
= 8 × 9 × 5
= 360
If you find it difficult to find the mistakes, check out the IPMAT Question Paper Analysis and Solutions to know the exact process.
Practice Question 3: The HCF of two numbers is 12, and their LCM is 252. If one of the numbers is 84, find the other number.
Answer: 36
Solution:
Using:
HCF × LCM = First number × Second number
12 × 252 = 84 × x
x = (12 × 252) / 84
x = 36
Practice Question 4: Three bells ring at intervals of 8, 12 and 18 minutes. If they ring together at 10:00 AM, after how much time will they ring together again?
Answer: 72 minutes
Solution:
LCM(8, 12, 18) = 72
Therefore, the bells will ring together again after 72 minutes, i.e. at 11:12 AM.
Practice Question 5: Find the greatest number that divides 72, 96 and 120 leaving the same remainder in each case.
Answer: 24
Solution:
When the same remainder is left, the divisor must divide the differences between the numbers.
96 − 72 = 24
120 − 96 = 24
Therefore:
HCF(24, 24) = 24
Useful Topic-Wise Resources
For targeted preparation, you can internally link relevant topic pages rather than sending students to a generic resource every time:
- IPMAT Study Material
- IPMAT Previous Year Papers
- IPMAT Ratio and Proportion Questions
- IPMAT Permutation and Combination Questions
- IPMAT Question Paper Analysis and Solutions
IPMAT HCF vs LCM Questions: What Is the Real Difference?
Most students get confused when asked about the difference between the HCF and LCM.
Here we have mentioned the possible differences between IPMAT HCF and LCM questions:
| HCF | LCM |
|---|---|
| Highest Common Factor | Least Common Multiple |
| Finds the greatest common divisor | Finds the smallest common multiple |
| Deals with factors | Deals with multiples |
| Usually gives a number no greater than the smallest given number | Usually gives a number no smaller than the largest given number |
| Useful in maximum grouping and equal distribution problems | Useful in repeating events and minimum-number problems |
For example, if a question asks for the greatest possible length into which several pieces can be divided equally, think HCF.
If it asks when several events will happen together again, think LCM.
How to Identify HCF and LCM Questions Quickly?
In an IPMAT exam, knowing the concept is only half the job. You also need to identify what the question is asking.
Look for these clues.
Words that usually indicate HCF
- greatest
- highest
- largest
- maximum
- greatest possible size
- equal pieces
- largest number that divides
- maximum groups
Words that usually indicate LCM
- least
- smallest
- minimum
- first time together
- next time together
- common interval
- smallest number divisible by
- events repeating at different intervals
For example:
“Find the greatest number that divides 48, 72 and 96 exactly.”
The word “greatest” and the phrase “divides exactly” immediately suggest HCF.
On the other hand:
“Three bells ring at intervals of 6, 8 and 12 minutes. When will they ring together again?”
The phrase “together again” points towards LCM.
Learning to spot these clues can save more time than memorising a long list of tricks.
Shortcuts to Solve IPMAT HCF and LCM Questions Faster
Although speed and accuracy matter the most while solving the questions, having a good grasp of shortcuts can really help boost scores.
| Shortcut | When to Use | Rule / Formula |
|---|---|---|
| 1. Co-prime Numbers | When two numbers have no common factor other than 1 | HCF = 1 LCM = Product of the numbers |
| 2. One Number Divides the Other | When one number is an exact multiple of the other | HCF = Smaller number; LCM = Larger number |
| 3. Use the Product Formula | When HCF, LCM and one of the two numbers are given | Other number = (HCF × LCM) ÷ Known number |
| 4. Check Differences in Remainder Questions | When the same remainder is left after dividing several numbers | Find the HCF of the differences between the given numbers |
| 5. Use Prime Powers Carefully | When solving HCF or LCM using prime factorisation | HCF → Lowest powers of common primes LCM → Highest powers of all primes |
IPMAT HCF and LCM Questions: Common Mistakes to Avoid
Mistake 1: Confusing HCF with LCM
“Greatest number that divides” generally points to HCF.
“Smallest number divisible by” generally points to LCM.
Read the wording before starting the calculation.
Mistake 2: Using the product formula for three numbers
The familiar relationship:
HCF × LCM = product of two numbers
is directly applicable to two numbers.
Do not automatically extend it to three or more numbers.
Mistake 3: Taking the wrong prime powers
For HCF, choose the lowest powers of the primes common to all numbers.
For LCM, choose the highest powers occurring across the numbers.
Mistake 4: Ignoring the remainder
It is recommended not to calculate the HCF and LCM of the original numbers blindly, especially in remainder problems
First, read and understand what the remainder condition implies.
Mistake 5: Overusing shortcuts
A shortcut is not a substitute for understanding the question.
If the numbers do not satisfy the condition required by a shortcut, switch to prime factorisation or another reliable method.
Conclusion
HCF and LCM aren’t hard because of the calculations. They get tricky when a familiar idea is hidden in a word problem.
So, the best way to prepare isn’t to memorise lots of separate tricks for each question; instead, learn the main relationships, spot common question patterns, and practice enough to quickly choose the right method.
As you practice IPMAT HCF and LCM questions, pay close attention to how the question is worded. Words like “greatest,” “maximum,” and “largest divisor” usually mean HCF, while “least,” “minimum,” and “together again” often mean LCM.
Once you get used to these patterns, HCF and LCM can become one of the fastest parts of your Number System revision.
Keep practising, review your mistakes, and use timed sets to get faster.
Plan Your Next Steps
Frequently Asked Questions
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Lalita Vishwakarma
Content Writer
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