NCERT Class 7 Maths Chapter 11
Finding Common Ground
This chapter from Ganita Prakash Part 2 focuses on HCF (Highest Common Factor) and LCM (Lowest Common Multiple) for CBSE Class 7 students, with an emphasis on understanding their relationship and applying them to solve real-life problems. Students use prime factorisation and the division method to find HCF and LCM and explore the relationship HCF × LCM = Product of two numbers.
Read Online
Key Terms
- HCF (Highest Common Factor)
- The greatest number that divides two or more numbers exactly without leaving a remainder. Also called the Greatest Common Divisor (GCD). For example, HCF of 12 and 18 is 6.
- LCM (Lowest Common Multiple)
- The smallest number that is a multiple of two or more numbers. For example, LCM of 4 and 6 is 12.
- Prime Factorisation
- Expressing a number as a product of its prime factors. For example, 36 = 2 × 2 × 3 × 3 = 2² × 3². Used to find HCF and LCM efficiently.
- Common Factor
- A number that is a factor of two or more given numbers. For example, common factors of 12 and 16 are 1, 2, and 4.
- Common Multiple
- A number that is a multiple of two or more given numbers. For example, common multiples of 3 and 4 include 12, 24, 36, etc.
- Co-prime Numbers
- Two numbers are co-prime (or relatively prime) if their HCF is 1. For example, 8 and 9 are co-prime because they share no common factor other than 1.
Frequently Asked Questions
What is the difference between HCF and LCM?▾
HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. LCM (Lowest Common Multiple) is the smallest number that both numbers divide into. For example, for 4 and 6: HCF = 2, LCM = 12.
How do you find the HCF using prime factorisation?▾
Write the prime factorisation of each number. Then identify the common prime factors and multiply them together, taking the smallest power of each. For example, HCF of 12 (= 2² × 3) and 18 (= 2 × 3²) is 2¹ × 3¹ = 6.
How do you find the LCM using prime factorisation?▾
Write the prime factorisation of each number. Then take all prime factors, using the highest power of each. For example, LCM of 12 (= 2² × 3) and 18 (= 2 × 3²) is 2² × 3² = 4 × 9 = 36.
What is the relationship between HCF and LCM?▾
For any two numbers a and b, HCF × LCM = a × b. This relationship is very useful — if you know the HCF and one of the numbers, you can find the LCM. For example, if HCF of 12 and 18 is 6, then LCM = (12 × 18) ÷ 6 = 216 ÷ 6 = 36.
Where is HCF used in real life?▾
HCF is used when we need to find the largest size of identical pieces that can be cut from two lengths (e.g., tiles for a floor), arrange objects in equal groups, or simplify fractions. LCM is used when finding when events that repeat at different intervals will coincide.
Disclaimer & Attribution
- All NCERT textbook PDFs displayed on this page are served directly from NCERT's official servers at ncert.nic.in. We do not host, store, or redistribute any PDF files on our servers.
- This website is free to use. We do not sell, charge for, or commercially exploit any NCERT content.
- All textbook content is the intellectual property of NCERT, Government of India and is published under their open-access policy for educational purposes.
- This page is provided purely for educational reference in compliance with NCERT's guidelines for non-commercial use of their freely available materials.