Class 7 Maths Part 2 Chapter 3, Finding Common Ground, explores prime factorisation, Highest Common Factor (HCF) and Lowest Common Multiple (LCM) through real-life floor-tiling and scheduling problems, prime-factor power rules, division procedures and the fundamental identity $\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b$.
What Class 7 Mathematics Chapter 3 Covers
3.1 The Greatest of All: Prime Factorisation & HCF uses square floor-tiling problems to motivate common factors and the Highest Common Factor (HCF), finds all factors via prime factorisation, and computes the HCF from common prime factors.
3.2–3.3 Least, but not Last (LCM) & Properties introduces the Lowest Common Multiple (LCM), computes HCF and LCM efficiently by the common division method, and proves that for any two positive integers $a$ and $b$, $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$.
Exercises in Chapter 3
- Figure it Out exercise sets and Summary with geometric and algebraic puzzles.
Read Class 7 Mathematics Chapter 3 Online
More Chapters
- Previous: Chapter 2: Operations with Integers
- Next: Chapter 4: Another Peek Beyond the Point
- All Mathematics chapters and the other Class 7 books: Class 7 NCERT books 2026-27
FAQ
How do you find the HCF and LCM of two numbers using their prime factorisations?
Write each number as a product of prime powers: the HCF is the product of the common prime factors raised to their smallest powers, while the LCM is the product of all prime factors involved raised to their highest powers.
What is the relationship between two numbers and their HCF and LCM?
For any two positive integers $a$ and $b$, the product of their HCF and LCM is equal to the product of the two numbers themselves: $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$.