- 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 pair of integers and verify that $LCM \times HCF =$ Product of two numbers : 36 and 64.
Given :
The given numbers are 36, 64.
To find :
We have to find LCM and HCF of the given numbers and verify that $LCM \times HCF of the two numbers = Product of the two numbers$.
Solution :
Prime factorisation of $36 = 2\times 2\times 3 \times 3 = 2^2 \times 3^2$
Prime factorisation of $64 = 2\times 2\times 2\times 2\times 2\times2 = 2^6$
HCF $=$ Product of smaller power of each common prime factor.
HCF $= 2^2 = 4 $.
LCM $=$ Product of highest power of each prime factor.
LCM $= 2^6\times 3^2$
$= 64 \times 9 $
LCM $= 576$
Verification :
If x and y are two numbers,
$$HCF (x, y) \times LCM (x, y) = Product of the two numbers (x \times y)$$
$HCF (36, 64) \times LCM (36, 64) = 36 \times 64$
$4 \times 576=36 \times 64 $
$2304 = 2304$
LHS $=$ RHS .
Therefore, It is verified that $HCF (36, 64) \times LCM (36, 64) = 36 \times 64$
28 Views
