- 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 pairs of integers and verify that LCM $\times$ HCF $=$ Product of the integers:
336 and 54
Given:
Given pair of integers is 336 and 54.
To do:
Here we have to find the LCM and HCF of the given pair of integers and then verify that LCM $\times$ HCF $=$ Product of the integers.
Solution:
Calculating LCM and HCF using prime factorization method:
Writing the numbers as a product of their prime factors:
Prime factorisation of 336:
- $2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 3\ \times\ 7\ =\ 2^4\ \times\ 3^1\ \times\ 7^1$
Prime factorisation of 54:
- $2\ \times\ 3\ \times\ 3\ \times\ 3\ =\ 2^1\ \times\ 3^3$
Multiplying the highest power of each prime number these values together:
$2^4\ \times\ 3^3\ \times\ 7^1\ =\ 3024$
LCM(336, 54) $=$ 3024
Multiplying all common prime factors:
$2^1\ \times\ 3^1\ =\ 6$
HCF(336, 54) $=$ 6
Now, verifying that LCM $\times$ HCF $=$ Product of the integers:
LCM $\times$ HCF $=$ Product of the integers
3024 $\times$ 6 $=$ 336 $\times$ 54
18144 $=$ 18144.
Advertisements