---
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entity_type: "chapter"
id: "69be809ebd8ab66187816aee"
title: "Finding Common Ground"
board: "CBSE"
curriculum: "CBSE"
class: "Class 7"
subject: "Mathematics"
book: "Ganita Prakash II"
chapter: "Finding Common Ground"
chapter_slug: "finding-common-ground"
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last_updated: "2026-06-20"
---

# Finding Common Ground

The chapter discusses methods of finding common factors and multiples using the example of tiles for a room and rice bags. It focuses on using prime factorization to make calculations easier and introduces concepts of Highest Common Factor (HCF) and Lowest Common Multiple (LCM).

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash II |
| Chapter | Finding Common Ground |
| Pages | 47-66 |

---

## Chapter Summary

### Short Summary
This chapter teaches how to find the largest square tiles to fit a room and the appropriate bag weights for rice from two farms using common factors, HCF, and LCM.

### Detailed Summary
The chapter begins with Sameeksha determining the size of square tiles for her room based on the dimensions given. It explains how to find common factors and emphasizes using HCF to minimize the number of tiles. Similarly, it discusses Lekhana's rice packing problem, showing how to employ prime factorization to find an optimal bag weight. The chapter provides examples to explain finding HCF and LCM, introducing concepts clearly and concisely with practical application scenarios.

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## Topic-Wise Explanation

### The Greatest of All
This section highlights the concept of HCF using the examples of tiles fitting in a room with dimensions of 12 ft by 16 ft, revealing common factors and their largest value.

### Finding Common Factors
This topic outlines techniques for determining common factors using two real-life scenarios, leading to understanding the HCF effectively.

### Using Prime Factorization
It details the method of prime factorization as a reliable way to find HCF and LCM, demonstrating the process with several numerical examples.

### Least, but not Last!
This section introduces the concept of LCM, explaining how to find the smallest common multiple for given lengths with practical examples.

### Finding the LCM through Prime Factorization
Focusing on identifying LCM through prime factorization, it emphasizes the importance of including the maximum instance of each prime factor in the final calculation.

### Patterns, Properties, and a Pretty Procedure!
The chapter concludes with general statements and conjectures about relationships in numbers, reinforcing the properties of HCF and LCM.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Highest Common Factor (HCF) | The greatest factor shared between two or more numbers. |
| Lowest Common Multiple (LCM) | The smallest multiple that two or more numbers share. |

---

## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Prime Factorization | Expressing a number as a product of its prime factors. |
| Common Factors | Factors that two or more numbers have in common. |

---

## Important Points for Revision

* The HCF of any two numbers is the greatest factor they share.
* The LCM of any two numbers is the smallest multiple they share.
* Prime factorization can simplify finding both HCF and LCM.
* An example of finding HCF through factorization is comparing 45 and 75.
* Understanding the order of prime factors does not change the product.
* Visual representation may aid in understanding problems involving HCF and LCM.
* Both HCF and LCM are useful in practical applications such as packing or dimensioning in real life.
* The chapter emphasizes problem-solving through systematic methods.

---

## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Conjecture | A statement that is proposed to be true based on observation but not yet proven. |

---

## Practice Questions

### Short Answer Questions
1. What is the HCF of 12 and 16?
2. How can prime factorization help find the LCM?
3. List the factors of 84.
4. What are the common factors of 84 and 108?
5. Explain what a conjecture is with an example.

### Long Answer Questions
1. Describe the process of finding the HCF of 45 and 75 using prime factorization.
2. Explain how to determine the LCM of 14 and 35 with examples.
3. Discuss the significance of using least common multiples in practical scenarios.

---

## Related Concepts

* Prime Numbers
* Factorization Methods
* Multiples and Factors

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69be809ebd8ab66187816aee |
| Canonical URL | https://www.edzy.ai/cbse-class-7-mathematics-ganita-prakash-ii-finding-common-ground |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-7-mathematics-ganita-prakash-ii-finding-common-ground.md |