Finding Common | Class 7 Mathematics Notes

Multiples and Common Multiples

This section delves into the formal definition of multiples and common multiples. A multiple of a number is defined as the product of that number and any integer. For example, multiples of 3 are 3, 6, 9, 12, and so on. The section explains how to list multiples of given numbers and identify common multiples by comparing these lists. It emphasizes that common multiples are numbers that appear in the multiples list of each number considered. The section also discusses that there are infinitely many multiples and hence infinitely many common multiples for any two numbers, but among them, the smallest positive common multiple is of special interest. This smallest positive common multiple is called the Least Common Multiple (LCM). The section provides examples to illustrate these concepts and explains the significance of finding common multiples in solving practical problems such as scheduling events that occur at different intervals.

📊 Diagram: The diagram shows two columns listing multiples of two numbers side by side, for example, multiples of 4 and 6, with common multiples highlighted. This visual aids in understanding how to identify common multiples by comparing lists.

🧪 Activity: Students are asked to list multiples of given numbers and identify common multiples to reinforce the concept.

🔗 Connection: This section sets the stage for the next section 'Finding the Least Common Multiple (LCM)' where methods to find the LCM are introduced.