Rahul Sir, a renowned aptitude trainer associated with OdTutor, has helped thousands of banking aspirants master quantitative aptitude concepts through logical methods and shortcut techniques. Among the most important topics in IBPS PO and Clerk examinations are Problems on H.C.F (Highest Common Factor) and L.C.M (Least Common Multiple). These concepts form the foundation of number systems and frequently appear in prelims and mains examinations.
Many candidates find H.C.F and L.C.M questions easy in theory but struggle with speed and accuracy during exams. Rahul Sir emphasizes understanding the relationship between factors and multiples instead of memorizing formulas blindly. Once students understand divisibility rules, prime factorization, and shortcut methods, they can solve complex questions within seconds.
In IBPS PO and Clerk exams, questions on H.C.F and L.C.M are often combined with word problems involving bells, events, workers, distribution, grouping, and repetitive cycles. A strong command of these concepts not only helps in direct questions but also improves performance in Number Series, Simplification, and Data Interpretation sections.
This guide covers practical tips, tricks, formulas, and examples that Rahul Sir recommends for mastering H.C.F and L.C.M. By following these techniques consistently and practicing regularly, aspirants can significantly improve their speed and confidence while attempting banking aptitude questions.
1. Understanding the Basics of H.C.F and L.C.M
Before learning shortcuts, students must clearly understand what H.C.F and L.C.M represent.
H.C.F (Highest Common Factor):
The greatest number that divides two or more numbers exactly.
L.C.M (Least Common Multiple):
The smallest number that is exactly divisible by two or more numbers.
Example:
Find H.C.F and L.C.M of 12 and 18.
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Common factors = 1, 2, 3, 6
Therefore:
H.C.F = 6
Multiples of 12 = 12, 24, 36, 48, 60…
Multiples of 18 = 18, 36, 54…
Common multiple = 36
L.C.M = 36
Understanding this basic concept is crucial because many aspirants jump directly to formulas without grasping the logic behind factors and multiples. Once the concept is clear, solving advanced banking questions becomes significantly easier.
Rahul Sir advises students to spend adequate time mastering these fundamentals before attempting shortcut techniques. Strong basics ensure fewer mistakes and faster calculations during competitive examinations.
2. Prime Factorization Method for Quick Solutions
Prime factorization is one of the most reliable methods for solving H.C.F and L.C.M questions.
Example:
Find H.C.F and L.C.M of 24 and 36.
Prime factors:
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
For H.C.F:
Take common factors with smallest powers.
H.C.F = 2² × 3
= 4 × 3
= 12
For L.C.M:
Take all factors with highest powers.
L.C.M = 2³ × 3²
= 8 × 9
= 72
This method is highly accurate and works well even for large numbers. Banking examinations frequently include questions where prime factorization provides the fastest path to the solution.
Students should memorize prime numbers up to at least 100 and practice factorizing numbers quickly. With sufficient practice, identifying prime factors becomes almost automatic.
Rahul Sir often recommends writing prime factors vertically because it reduces confusion and calculation errors. This systematic approach ensures maximum accuracy under exam pressure.
3. Product Formula Trick
One of the most important formulas in aptitude exams is:
H.C.F × L.C.M = Product of the Numbers
For two numbers:
HCF × LCM = First Number × Second Number
Example:
Two numbers are 24 and 36.
HCF = 12
LCM = ?
LCM = (24 × 36)/12
= 864/12
= 72
This formula is frequently used in IBPS examinations.
Example:
H.C.F = 8
LC.M = 120
One number = 24
Find the other number.
8 × 120 = 24 × Other Number
960 = 24 × Other Number
Other Number = 40
Questions based on this concept are very common because they test conceptual understanding rather than lengthy calculations.
Rahul Sir advises students to immediately identify opportunities to use this formula, as it can save valuable exam time and eliminate unnecessary calculations.
4. Shortcut for Finding H.C.F Using Division Method
The division method is extremely useful when dealing with large numbers.
Example:
Find H.C.F of 84 and 126.
126 ÷ 84 = 1 remainder 42
84 ÷ 42 = 2 remainder 0
Therefore,
H.C.F = 42
This method is much faster than writing all factors.
Example:
Find H.C.F of 198 and 252.
252 ÷ 198 = remainder 54
198 ÷ 54 = remainder 36
54 ÷ 36 = remainder 18
36 ÷ 18 = 0
Therefore,
H.C.F = 18
The division method is particularly useful in banking exams where speed matters. Students should practice this technique regularly because it can solve large-number questions within seconds.
Rahul Sir recommends performing rough calculations mentally while using the division method to reduce dependence on written work and increase speed during examinations.
5. Solving Word Problems Based on L.C.M
Many IBPS questions involve repetitive events.
Example:
Two bells ring every 12 minutes and 18 minutes.
If they ring together now, after how many minutes will they ring together again?
L.C.M of 12 and 18
12 = 2² × 3
18 = 2 × 3²
L.C.M = 36
Answer = 36 minutes
Such questions appear frequently in banking exams.
Common applications include:
- Bells ringing
- Traffic signals
- Workers completing cycles
- Machines operating repeatedly
- Events occurring at fixed intervals
The key is recognizing that whenever events repeat at different intervals and meet again, L.C.M is generally required.
Rahul Sir teaches students to immediately identify keywords like “together again,” “simultaneously,” and “after how long” as indicators that L.C.M may be involved.
6. Distribution and Grouping Problems Using H.C.F
H.C.F is commonly used when items must be distributed into maximum equal groups.
Example:
96 chocolates and 144 candies are to be packed into identical packets.
Find the maximum number of packets.
H.C.F of 96 and 144:
96 = 2⁵ × 3
144 = 2⁴ × 3²
H.C.F = 2⁴ × 3
= 48
Answer = 48 packets
Each packet contains:
96/48 = 2 chocolates
144/48 = 3 candies
Whenever questions ask for:
- Greatest possible groups
- Maximum equal distribution
- Largest size of groups
Think about H.C.F.
These problems are very popular in competitive examinations because they test practical understanding of factors.
Regular practice helps students identify such questions instantly and apply the correct approach without confusion.
7. Relationship Between H.C.F and L.C.M in Exam Questions
Banking exams frequently ask conceptual questions.
Example:
H.C.F of two numbers is 12 and L.C.M is 720.
If one number is 144, find the other.
Using:
H.C.F × L.C.M = Product of Numbers
12 × 720 = 144 × Other Number
8640 = 144 × Other Number
Other Number = 60
Questions based on this relationship often appear in IBPS prelims and mains because they require both conceptual clarity and calculation speed.
Students should memorize this formula thoroughly because it eliminates lengthy factorization methods.
Rahul Sir suggests solving at least 50 such problems before the exam to develop confidence and familiarity with different variations.
8. Common Mistakes Students Make
Many candidates lose marks due to avoidable mistakes.
Common errors include:
- Confusing H.C.F with L.C.M
- Missing prime factors
- Using highest powers for H.C.F
- Using lowest powers for L.C.M
- Calculation mistakes during multiplication
Example:
24 = 2³ × 3
36 = 2² × 3²
Incorrect H.C.F = 72
Correct H.C.F = 12
Students should carefully remember:
For H.C.F → Lowest powers.
For L.C.M → Highest powers.
Another mistake is rushing through calculations. Even when concepts are clear, careless arithmetic errors can lead to wrong answers.
Rahul Sir emphasizes maintaining a balance between speed and accuracy. A correct answer in 20 seconds is better than a wrong answer in 10 seconds.
9. Fast Calculation Techniques for IBPS Exams
Speed plays a crucial role in banking exams.
Useful techniques include:
- Memorize prime numbers.
- Learn divisibility rules.
- Practice multiplication tables up to 30.
- Memorize squares up to 50.
- Memorize cubes up to 20.
Example:
Find L.C.M of 15 and 20.
15 = 3 × 5
20 = 2² × 5
LCM = 2² × 3 × 5
= 60
With practice, students can mentally identify factors without writing every step.
Another useful trick is cancellation during multiplication to avoid large calculations.
Regular timed practice improves efficiency significantly and helps candidates complete aptitude sections faster.
Rahul Sir recommends solving at least 20 H.C.F and L.C.M questions daily for two weeks before the examination.
10. Exam-Oriented Strategy for H.C.F and L.C.M Questions
Success in IBPS exams depends on strategy as much as knowledge.
Recommended approach:
- Read carefully.
- Identify whether H.C.F or L.C.M is required.
- Use the fastest method.
- Verify calculations.
- Move on quickly.
Example:
Three lights blink every 6, 8, and 12 seconds.
When will they blink together again?
LCM:
6 = 2 × 3
8 = 2³
12 = 2² × 3
LCM = 2³ × 3
= 24
Answer = 24 seconds
Questions like these should ideally take less than one minute.
Students should create formula sheets and revise them regularly. Mock tests help identify weak areas and improve time management. Consistent practice, conceptual understanding, and shortcut techniques can make H.C.F and L.C.M one of the highest-scoring topics in the aptitude section.
How Teachers from OdTutor Can Help
At OdTutor, Rahul Sir and the expert aptitude faculty provide structured training for IBPS PO and Clerk aspirants. Students receive concept-based lessons, shortcut techniques, exam-oriented practice sets, mock tests, and doubt-solving sessions specifically designed for banking examinations. Teachers focus on improving calculation speed, accuracy, and question selection strategies. Regular assignments and previous-year question discussions help students understand actual exam patterns. Whether you are a beginner or an advanced learner, OdTutor’s personalized guidance ensures that topics like H.C.F and L.C.M become scoring areas. With expert mentorship and continuous practice support, students can significantly improve their quantitative aptitude performance and increase their chances of success in competitive banking exams.