Check if LCM of array elements is divisible by a prime number or not

• Difficulty Level : Medium
• Last Updated : 25 Jun, 2022

Given an array and a number k, the task is to find if LCM of the array is divisible by k or not.
Examples :

```Input : int[] a = {10, 20, 15, 25}
k = 3
Output : true

Input : int[] a = {24, 21, 45, 57, 36};
k = 23;
Output : false```

One simple solution is to first find LCM of array elements, then check if LCM is divisible by k or not.
Here, without calculating the LCM of the number we can find that LCM of the an array of number is divisible by a prime number k or not. If any number of the array is divisible by prime number k, then the LCM of the number is also divisible by prime number k.

C++

 `// C++ program to find LCM of``// array of number is divisible``// by a prime number k or not``#include``using` `namespace` `std;` `// Function to check any number of``// array is divisible by k or not``bool` `func(``int` `a[], ``int` `k, ``int` `n)``{``    ``// If any array element is divisible``    ``// by k, then LCM of whole array``    ``// should also be divisible.``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(a[i] % k == 0)``        ``return` `true``;``    ``return` `false``;``}` `// Driver Code``int` `main()``{``    ``int` `a[] = {14, 27, 38, 76, 84};``    ``int` `k = 19;``    ``bool` `res = func(a, k, 5);``    ``if``(res)``    ``cout<<``"true"``;``    ``else``    ``cout<<``"false"``;``    ``return` `0;``}` `// This code is contributed``// by Mr. Somesh Awasthi`

Java

 `// Java program to find LCM of``// array of number is divisible``// by a prime number k or not``import` `java.lang.*;``import` `java.util.*;` `class` `GFG``{``    ``// Function to check any number``    ``// of array is divisible by k or not``    ``static` `boolean` `func( ``int` `a[], ``int` `k)``    ``{``        ``// If any array element is divisible``        ``// by k, then LCM of whole array``        ``// should also be divisible.``        ``for` `(``int` `i = ``0``; i < a.length; i++)``            ``if` `(a[i] % k == ``0``)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int``[] a = {``14``, ``27``, ``38``, ``76``, ``84``};``        ``int` `k = ``19``;``        ``boolean` `res = func(a, k);``        ``System.out.println(res);``    ``}``}`

Python 3

 `# Python 3 program to find LCM``# of array of number is divisible``# by a prime number k or not`  `# Function to check any number of``# array is divisible by k or not``def` `func( a, k, n) :``    ` `    ``# If any array element is``    ``# divisible by k, then LCM``    ``# of whole array should also``    ``# be divisible.``    ``for` `i ``in` `range``(``0``, n) :``        ``if` `( a[i] ``%` `k ``=``=` `0``):``            ``return` `True`  `# Driver Code``a ``=` `[``14``, ``27``, ``38``, ``76``, ``84``]``k ``=` `19``res ``=` `func(a, k, ``5``)` `if``(res) :``    ``print``(``"true"``)``else` `:``    ``print``(``"false"``)``    `   `# This code is contributed``# by Nikita Tiwari.`

C#

 `// C# program to find LCM of array``// of number is divisible by a prime``// number k or not``using` `System;` `class` `GFG``{``    ` `    ``// Function to check any number of``    ``// array is divisible by k or not``    ``static` `bool` `func(``int` `[]a, ``int` `k)``    ``{``        ` `        ``// If any array element is``        ``// divisible by k, then LCM``        ``// of whole array should also``        ``// be divisible.``        ``for` `(``int` `i = 0; i < a.Length; i++)``            ``if` `(a[i] % k == 0)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[]a = {14, 27, 38, 76, 84};``        ``int` `k = 19;``        ``bool` `res = func(a, k);``        ``Console.Write(res);``    ``}``}` `// This code is contributed by nitin mittal.`

PHP

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Javascript

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Output :

` true`

Time Complexity: O(n)
Auxiliary Space: O(1)

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