Problems on H.C.F and L.C.M
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Study MaterialProblems on H.C.F and L.C.M Cheat Sheet
H.C.F (Highest Common Factor) and L.C.M (Lowest Common Multiple) are among the most important topics in Quantitative Aptitude and are frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand HCF and LCM concepts, factorization methods, Euclidean algorithm, relationship formulas, fraction and decimal applications, and shortcut tricks for solving exam-oriented questions quickly and accurately.
About This Cheat Sheet
Complete guide to H.C.F and L.C.M for competitive exams:
Methods to Find HCF
- Prime Factorization Method
- Division Method
- Euclidean Algorithm
- Common Factor Method
Methods to Find LCM
- Prime Factorization Method
- Division Method
- Multiple Method
- Shortcut Techniques
Important Relationships
- HCF × LCM = Product of Numbers
- Relation for Two Numbers
- Co-prime Number Concepts
- Divisibility Properties
HCF & LCM of Fractions
Methods to calculate HCF and LCM for fractional values using numerator and denominator rules.
HCF & LCM of Decimals
- Decimal Conversion Method
- Removing Decimal Places
- Fraction Conversion Tricks
- Shortcut Calculations
Word Problems on HCF
- Greatest Length Problems
- Greatest Capacity Problems
- Largest Divisor Questions
- Equal Distribution Problems
Word Problems on LCM
- Smallest Number Problems
- Least Time Problems
- Simultaneous Events
- Repeated Interval Questions
Shortcut Tricks
Fast calculation methods, prime factorization shortcuts, and exam-oriented problem-solving techniques.
Topics Covered
| Topic | Description |
|---|---|
| HCF Basics | Highest common factor of two or more numbers |
| LCM Basics | Least common multiple of given numbers |
| Prime Factorization | Finding HCF and LCM using prime factors |
| Division Method | Step-by-step division approach |
| Euclidean Algorithm | Efficient method to calculate HCF |
| Relationship Formula | Product of numbers = HCF × LCM |
| Co-prime Numbers | Numbers having HCF equal to 1 |
| HCF of Fractions | Rules to find HCF for fractions |
| LCM of Fractions | Methods to calculate LCM of fractions |
| HCF & LCM of Decimals | Techniques for decimal-based calculations |
| Greatest Divisor Problems | Word problems involving maximum divisibility |
| Least Time Problems | LCM-based simultaneous event questions |
| Greatest Length Problems | Cutting and arrangement-based questions |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Core Concepts
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Improve Calculation Speed
↓
Apply Shortcut Techniques
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Solve Word Problems Faster
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Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Example
Example:
Find the HCF and LCM of 12 and 18.
Prime factors of 12 = 2 × 2 × 3
Prime factors of 18 = 2 × 3 × 3
HCF = Common factors = 2 × 3 = 6
LCM = Product of highest powers = 2 × 2 × 3 × 3 = 36
Answer:
HCF = 6
LCM = 36
Final Takeaway
This Problems on H.C.F and L.C.M Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of factorization methods, relationship formulas, decimal applications, and word problems can significantly improve speed, accuracy, and logical problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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