- 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:
510 and 92
Given:
Given pair of integers is 510 and 92.
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 510:
- $2\ \times\ 3\ \times\ 5\ \times\ 17\ =\ 2^1\ \times\ 3^1\ \times\ 5^1\ \times\ 17^1$
Prime factorisation of 92:
- $2\ \times\ 2\ \times\ 23\ =\ 2^2\ \times\ 23^1$
Multiplying the highest power of each prime number these values together:
$2^2\ \times\ 3^1\ \times\ 5^1\ \times\ 17^1\ \times\ 23^1\ =\ 23460$
LCM(510, 92) $=$ 23460
Multiplying all common prime factors:
$2^1\ =\ 2$
HCF(510, 92) $=$ 2
Now, verifying that LCM $\times$ HCF $=$ Product of the integers:
LCM $\times$ HCF $=$ Product of the integers
23460 $\times$ 2 $=$ 510 $\times$ 92
46920 $=$ 46920.