# Print N lines of 4 numbers such that every pair among 4 numbers has a GCD K

Given N and K, the task is to print N lines where each line contains 4 numbers such that every among those 4 numbers has a GCD K and the maximum number used in N*4 should be minimized.

**Note:** In case of multiple outputs, print any one.

**Examples:**

Input:N = 1, K = 1

Output: 1 2 3 5

Every pair among 1, 2, 3 and 5 gives a GCD K and the largest number among these is 5 which the minimum possible.

Input: 2 2

Output:

2 4 6 22

14 18 10 16In the above input, the maximum number is 22, which is the minimum possible to make 2 lines of 4 numbers.

**Approach: **The first observation is that if we can solve the given problem for K=1, we can solve the problem with GCD K by simply multiplying the answers with K. We know that any three consecutive odd numbers have a GCD 1 always when paired, so three numbers of every line can be easily obtained. Hence the lines will look like:

1 3 5 _ 7 9 11 _ 13 15 17 _ . . .

An even number cannot be inserted always, because inserting 6 in third line will give GCD(6, 9) as 3. So the best number that can be inserted is a number between the first two off numbers of every line. Hence the pattern looks like:

1 2 3 5 7 8 9 11 13 14 15 17 . . .

To obtain given GCD K, one can easily multiply K to the obtained numbers. Hence for i-th line:

- the first number will be k * (6*i+1)
- the second number will be k * (6*i+1)
- the third number will be k * (6*i+3)
- the fourth number will be k * (6*i+5)

The maximum number among N*4 numbers will be **k * (6*i – 1) **

Below is the implementation of the above approach.

## C++

`// C++ implementation of the ` `// above approach ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to print N lines ` `void` `printLines(` `int` `n, ` `int` `k) ` `{ ` ` ` `// Iterate N times to print N lines ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` `cout << k * (6 * i + 1) << ` `" "` ` ` `<< k * (6 * i + 2) << ` `" "` ` ` `<< k * (6 * i + 3) << ` `" "` ` ` `<< k * (6 * i + 5) << endl; ` ` ` `} ` `} ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 2, k = 2; ` ` ` `printLines(n, k); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java implementation of the ` `// above approach ` ` ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` ` `class` `GFG ` `{ ` `// Function to print N lines ` `static` `void` `printLines(` `int` `n, ` `int` `k) ` `{ ` ` ` `// Iterate N times to print N lines ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) { ` ` ` `System.out.println ( k * (` `6` `* i + ` `1` `) + ` `" "` ` ` `+ k * (` `6` `* i + ` `2` `) + ` `" "` ` ` `+ k * (` `6` `* i + ` `3` `) + ` `" "` ` ` `+ k * (` `6` `* i + ` `5` `) ); ` ` ` `} ` `} ` `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` ` ` `int` `n = ` `2` `, k = ` `2` `; ` ` ` `printLines(n, k); ` `} ` `} ` |

*chevron_right*

*filter_none*

## Python 3

`# Python implementation of the ` `# above approach. ` ` ` `# Function to print N lines ` `def` `printLines(n, k) : ` ` ` ` ` `# Iterate N times to print N lines ` ` ` `for` `i ` `in` `range` `(n) : ` ` ` `print` `( k ` `*` `(` `6` `*` `i ` `+` `1` `), ` ` ` `k ` `*` `(` `6` `*` `i ` `+` `2` `), ` ` ` `k ` `*` `(` `6` `*` `i ` `+` `3` `), ` ` ` `k ` `*` `(` `6` `*` `i ` `+` `5` `)) ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `n, k ` `=` `2` `, ` `2` ` ` `printLines(n, k) ` ` ` `# This code is contributed by ANKITRAI1 ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// Function to print N lines ` `function` `printLines(` `$n` `, ` `$k` `) ` `{ ` ` ` `// Iterate N times to print N lines ` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++) ` ` ` `{ ` ` ` `echo` `(` `$k` `* (6 * ` `$i` `+ 1)); ` ` ` `echo` `(` `" "` `); ` ` ` `echo` `(` `$k` `* (6 * ` `$i` `+ 2)); ` ` ` `echo` `(` `" "` `); ` ` ` `echo` `(` `$k` `* (6 * ` `$i` `+ 3)); ` ` ` `echo` `(` `" "` `); ` ` ` `echo` `(` `$k` `* (6 * ` `$i` `+ 5)); ` ` ` `echo` `(` `"\n"` `); ` ` ` `} ` `} ` ` ` `// Driver Code ` `$n` `= 2; ` `$k` `= 2; ` `printLines(` `$n` `, ` `$k` `); ` ` ` `// This code is contributed ` `// by Shivi_Aggarwal ` `?> ` |

*chevron_right*

*filter_none*

## C#

`// C# implementation of the ` `// above approach ` `using` `System; ` ` ` `class` `GFG ` `{ ` `// Function to print N lines ` `static` `void` `printLines(` `int` `n, ` `int` `k) ` `{ ` ` ` `// Iterate N times to print N lines ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `Console.WriteLine ( k * (6 * i + 1) + ` `" "` `+ ` ` ` `k * (6 * i + 2) + ` `" "` `+ ` ` ` `k * (6 * i + 3) + ` `" "` `+ ` ` ` `k * (6 * i + 5) ); ` ` ` `} ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `n = 2, k = 2; ` ` ` `printLines(n, k); ` `} ` `} ` ` ` `// This code is contributed ` `// by Akanksha Rai(Abby_akku) ` |

*chevron_right*

*filter_none*

**Output:**

2 4 6 10 14 16 18 22

**Time Complexity:** O(4*N)

## Recommended Posts:

- Check if the given two numbers are friendly pair or not
- Find original numbers from gcd() every pair
- Pair of prime numbers with a given sum and minimum absolute difference
- Print numbers such that no two consecutive numbers are co-prime and every three consecutive numbers are co-prime
- Print first N Mosaic numbers
- Print numbers with digits 0 and 1 only such that their sum is N
- Print the kth common factor of two numbers
- Print all Good numbers in given range
- Print prime numbers in a given range using C++ STL
- Program to print first n Fibonacci Numbers | Set 1
- Print squares of first n natural numbers without using *, / and -
- Print all numbers less than N with at-most 2 unique digits
- Program to print non square numbers
- Print n numbers such that their sum is a perfect square
- Print all integers that are sum of powers of two given numbers

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.