Class 7 Maths (Part II) Chapter 3 : Finding Common Ground | HCF, LCM, Prime Factorization & Real-Life Problems 2025
Complete Chapter 3 (Part II) guide: finding Highest Common Factor (HCF) for tiling floors and packing rice bags, finding Lowest Common Multiple (LCM) for cloth torans and 'Jump Jackpot' games, using prime factorization (division method and factor trees) to find HCF and LCM easily, solving word problems involving scheduling (sweet shop visit) and resource optimization, plus solved examples and practice questions for CBSE Class 7 Maths
Updated: 6 months ago

Finding Common Ground
Class 7 Mathematics Chapter 3 | Complete Guide | HCF and LCM 2025
Chapter at a Glance – Finding Common Ground
This chapter explores Highest Common Factor (HCF) and Lowest Common Multiple (LCM) using real-life examples, prime factorization, and properties.
Main Topics Covered
- HCF using tile and rice bag examples
- Prime numbers and prime factorization
- Finding factors using prime factorization
- HCF using prime factorization
- LCM using toran and gajak examples
- LCM using prime factorization
- Patterns and properties of HCF and LCM
- Efficient procedures for HCF and LCM
- Relationship between HCF and LCM
- Conjectures, generalizations, and counterexamples
Key Takeaways for Exams
HCF Definition
Highest common factor of numbers.
LCM Definition
Lowest common multiple of numbers.
Prime Factorization
Break down into primes.
HCF Method
Min exponents of common primes.
LCM Method
Max exponents of all primes.
Property
HCF × LCM = Product of numbers.
Division Method
For prime factorization.
Efficient Procedure
Divide by common factors for HCF/LCM.



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