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 smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.
Given :
The smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.
To find :
We have to find the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.
Solution :
The smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30 is a multiple of the LCM of the given numbers.
LCM of 16, 18, 24 and 30 is,
| 2 | 16,18,24,30 |
| 2 | 8,9,12,15 |
| 2 | 4,9,6,15 |
| 3 | 2,9,3,15 |
| 2 | 2,3,1,5 |
| 3 | 1,3,1,5 |
| 1,1,1,5 |
$LCM=2\times 2\times 2\times 2\times 3\times 3\times 5=2^{4} \times 3^{2} \times 5=16\times 9\times 5=144\times 5=720$
Multiples of 720 are $720\times1=720,720\times2=1440,....720\times14=10080$
Therefore, the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30 is 10080.
Updated on: 10-Oct-2022
9K+ Views
Advertisements