Multiples
2026-02-28 01:00 Diff

We have now learned the importance of understanding multiples in general. Next, we will discuss how students can apply their knowledge of multiples in mathematics. Learning multiples lays the foundation for other complex concepts in math. 


Here are a few applications of multiples in math:


Factors and Multiples


Factors and multiples are distinct yet interconnected concepts. What is a factor? They are the numbers that divide a given number exactly without any remainder. Whereas, multiples of a number are the products we get from multiplying the given number with a set of natural numbers. Understanding multiples helps students recognize the patterns in numbers.


For example:
Take the number 8
The factors of 8 are 1, 2, 4, and 8
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, and so on…


Highest Common Factor (HCF) Using Multiples


The HCF of two or more numbers is the largest common factor dividing the given numbers completely. HCF is found by listing factors, not multiples. Example: Factors of 15 are 1, 3, 5, and 15. Factors of 25 are 1, 5, and 25. The common factor is 5.

The Least Common Multiple (LCM) Using Multiples


The LCM or the least common multiple, is the smallest number by which two or more numbers can be completely divided.


For example: We find the LCM of 6 and 8
Multiples of 6 are 6, 12, 18, 24,...
Multiples of 8 are 8, 16, 24, 32,...
Considering the common multiples, we get 24 as the LCM of 6 and 8.


Prime Factorization and Multiples


prime factorization is an important method to find factors and multiples. Then what is prime factorization? Prime factorization of a number is the process of dividing a given number into its prime factors. This helps us in determining its multiples. We obtain multiples in the process of multiplying the prime factors with natural numbers.
 

What is a prime factor? 
Prime factors are the prime numbers that exactly divide a given number, leaving no remainder.


For example: The prime factorization of 46 is 2 × 23. Both 2 and 23 are prime numbers.

Multiples of 46 are 46, 92, 138, 184,...