HCF and LCM
HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental topics in number system aptitude. They are widely used in solving problems related to divisibility, fractions, time cycles, and word problems in competitive exams.
Fundamental Principles
HCF (Highest Common Factor)
The greatest number that divides two or more numbers exactly without leaving a remainder.
LCM (Least Common Multiple)
The smallest number that is a multiple of two or more numbers.
Relationship Formula
For two numbers: HCF × LCM = Product of the numbers.
Essential Formulation Tips
- Use prime factorization for large numbers.
- For two numbers, always remember: HCF × LCM = Product.
- HCF is always less than or equal to the smallest number.
- LCM is always greater than or equal to the largest number.
Shortcut Execution Techniques
- Use division method for faster HCF calculation.
- For co-prime numbers, HCF = 1 and LCM = product of numbers.
- To find LCM quickly, take highest powers of all prime factors.
- Use shortcut: LCM = (Product of numbers) / HCF.
Contextual Inquiries (FAQs)
Q: What is the fastest way to find HCF?
A:
Q: When do we use LCM in real life problems?
A:
Example Breakdown: HCF Example
Basic HCF question.Prime factorization:
24 = 2 × 2 × 2 × 3.
36 = 2 × 2 × 3 × 3.
Common factors = 2 × 2 × 3 = 12.
Final Answer: 12.
Example Breakdown: LCM Example
Most repeated exam question.Prime factorization:
4 = 2², 6 = 2 × 3.
Take highest powers: 2² × 3 = 12.
Final Answer: 12.
Example Breakdown: HCF-LCM Relation Example
Important shortcut question.Use formula: HCF × LCM = Product.
6 × LCM = 180.
LCM = 180 / 6 = 30.
Final Answer: 30.
HCF & LCM Practice Questions
Solve important HCF and LCM questions for banking, SSC, CMAT, and placement exams.
Q1. Find HCF of 18 and 27.
Q2. Find LCM of 8 and 12.
Q3. If HCF = 4 and LCM = 60, find product of numbers.