- 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 greatest number of 6 digits exactly divisible by 24, 15 and 36./p>

**Given:** 24, 15 and 36.

**To find:** Here we have to find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

**Solution:**

The greatest 6-digit number $=$ 999999

LCM is the least common multiple of any three numbers and to find the greatest 6-digit number we have to check if 999999 is divisible by the LCM of 24, 15 and 36.

__Now, calculating LCM of 24, 15 and 36 using prime factorization method__:

Writing the numbers as a product of their prime factors:

Prime factorization of 24:

- $2\ \times\ 2\ \times\ 2\ \times\ 3\ =\ 2^3\ \times\ 3^1$

Prime factorization of 15:

- $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$

Prime factorization of 36:

- $2\ \times\ 2\ \times\ 3\ \times\ 3\ =\ 2^2\ \times\ 3^2$

Multiplying highest power of each prime number:

- $2^3\ \times\ 3^2\ \times\ 5^1\ =\ 360$

LCM(24, 15, 36) $=$ **360**

Now,

$999999\ =\ 360\ \times\ 2777\ +\ 279$

Here remainder is 279. So,

Required number $=$ 999999 $-$ 279 $=$ ** 999720**

So, the greatest 6 digit number which is exactly divisible by 24, 15 and 36 is 999720.

- Related Articles
- Find the greatest 3 digit number that is exactly divisible by 6 15 and 21
- Find the least number divisible by 15, 20, 24, 32, and 36.
- Find the smallest 4 digit number which is exactly divisible by 18, 24, 36.
- Find the digits p and q, if the number p7q6 is divisible by 24.
- Find the greatest 5 digit number that is exactly divisible by 22,25 and 30
- Find the smallest 4 digit number that is exactly divisible by 36, 40, and 45.
- Determine the greatest 3 digit number exactly divisible by 8, 10, and 12.
- Find the smallest number which when reduced by 3 is divisible by 24, 36 and 40.
- Find the least square number, exactly divisible by each one of the numbers:(i) 6, 9, 15 and 20(ii) 8, 12, 15 and 20.
- Determine the greatest four-digit number which is exactly divisible by 10,12,16.?
- Find the greatest 3 digit number which is divisible by the number 4 ,5 and 6.
- Find the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.
- What is the least square number which is exactly divisible by each of these numbers 6, 9, 15, and 20?
- Find the least number which is exactly divisible by 10, 15, 20 and also a perfect square.
- Find the greatest number that exactly divides 289 and 391.