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

Categories: Class 7 Mathematics, NCERT Maths Notes 2025, Factors & Multiples, HCF & LCM Applications, CBSE Exam Preparation, Practice Questions & Quizzes
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Class 7 Mathematics Chapter 3: Finding Common Ground – HCF and LCM Complete Notes, Solutions, Questions & Answers 2025

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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