- 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

# Which is the smallest 4-digit number divisible by 8, 10 and 12?

__Given__:

8, 10 and 12

__
__

__To find__:

We have to find the smallest 4-digit number divisible by 8, 10 and 12

__
__

__
__

__Solution__:

To find the smallest 4 digit number which is exactly divisible by 8, 10 and 12, we have to first find the LCM of 8, 10 and 12:

$8\ =\ 2\ \times \ 2\ \times \ 2$

$10\ =\ 2\ \times \ 5$

$12\ =\ 2\ \times \ 2\ \times \ 3$

LCM = 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 5 = 120

So, LCM of 8, 10 and 12 is 120. But we want the least 4 digit number, which is exactly divisible by 8, 10 and 12.

Smallest 4 digit number = 1000.

Now,

$1000\ =\ ( 8\ \times \ 120) \ +\ 40$

Next higher quotient is 9.

So, the required number = 9 × 120 = 1080

Hence, the required number is 1080, which is exactly divisible by 8, 10 and 12.