- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Find the LCM and HCF of the following integers by applying the prime factorization method:

24, 15 and 36

Given: 24, 15 and 36.

To find: Here we have to find the LCM and HCF of the given integers by applying the prime factorization method.

Solution:

__Calculating LCM and HCF using prime factorization method__:

Writing the numbers as a product of their prime factors:

Prime factorisation of 24:

- $2\ \times\ 2\ \times\ 2\ \times\ 3\ =\ 2^3\ \times\ 3^1$

Prime factorisation of 15:

- $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$

Prime factorisation of 36:

- $2\ \times\ 2\ \times\ 3\ \times\ 3\ =\ 2^2\ \times\ 3^2$

Multiplying the highest power of each prime number these values together:

$2^3\ \times\ 3^2\ \times\ 5^1\ =\ 360$

LCM(24, 15, 36) $=$ 360

Multiplying all common prime factors:

$3^1\ =\ 3$

HCF(24, 15, 36) $=$ 3

So, the LCM and HCF of 24, 15 and 36 are 360 and 3 respectively.

Advertisements