- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- 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 least number which when divided by 6,15 and 18 leave remainder 5 in each case.

Given:

6, 15 and 18.

To do:

We have to find the smallest number that when divided by 6, 15 and 18 leaves a remainder of 5 in each case.

Solution:

The smallest number that when divided by 6, 15 and 18 leaves a remainder of 0 in each case is the LCM of 6, 15 and 18.

So,

The smallest number that when divided by 6, 15 and 18 leaves a remainder of 5 in each case is $=$ LCM of 6, 15 and 18 $+$ 5

Now,

Finding LCM of 6, 15 and 18:

Writing all the numbers as a product of their prime factors:

Prime factorization of 6:

$6=2\times3$

Prime factorization of 15:

$15=3\times5$

Prime factorization of 18:

$18=2\times3\times3$

LCM of 6, 15 and 18 $=2\times3\times3\times5$

$=90$

Thus,

LCM$(6, 15, 18) = 90$

The smallest number that when divided by 6, 15 and 18 leaves a remainder of 5 in each case is $=$ LCM of 6, 15 and 18 $+$ 5

The least number that when divided by 6, 15 and 18 leaves a remainder of 5 in each case is $=90+5$

$=95$

The least number that when divided by 6, 15 and 18 leaves a remainder of 5 in each case is 95.

- Related Questions & Answers
- Program to find remainder when large number is divided by 11 in C++
- Program to find remainder when large number is divided by r in C++
- C++ program to find Nth number of the series 1, 6, 15, 28, 45, …..
- C++ program to find Nth term of the series 1, 6, 18, 40, 75, ….
- MySQL ORDER BY with CASE WHEN
- Program to find N-th term of series 3, 6, 18, 24, … in C++
- Multiply a number by 15 without using * and / operators in C++
- Find permutation of n which is divisible by 3 but not divisible by 6 in C++
- How To Fix and Protect The Linux Server Against the Dirty COW Vulnerability on CentOS 5/6/7 or RHEL 5/6/7
- Find sum of the series 1-2+3-4+5-6+7....in C++
- Golang Program to Find the Numbers which are Divisible by 7 and Multiple of 5 in a Given Range
- Program to find remainder after dividing n number of 1s by m in Python
- When are you supposed to leave a job?
- Find reminder of array multiplication divided by n in C++
- CASE WHEN in PostgreSQL?
- PHP program to find the first natural number whose factorial can be divided by a number ‘x’