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

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  • Difficulty Level : Medium
  • Last Updated : 25 Jun, 2022
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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<iostream>
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




<?php
// PHP 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
function func( $a, $k, $n)
{
    // If any array element is divisible
    // by k, then LCM of whole array
    // should also be divisible.
    for ($i = 0; $i < $n; $i++)
        if ($a[$i] % $k == 0)
        return true;
    return false;
}
 
// Driver Code
$a = array(14, 27, 38, 76, 84);
$k = 19;
$res = func($a, $k, 5);
 
if($res)
echo"true";
else
echo"false";
 
// This code is contributed by nitin mittal
?>

Javascript




<script>
// javascript 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
    function func(a , k)
    {
     
        // If any array element is divisible
        // by k, then LCM of whole array
        // should also be divisible.
        for (let i = 0; i < a.length; i++)
            if (a[i] % k == 0)
                return true;
        return false;
    }
 
    // Driver Code
     
        let a = [ 14, 27, 38, 76, 84 ];
        var k = 19;
        let res = func(a, k);
        document.write(res);
 
 
// This code is contributed by todaysgaurav
</script>

Output : 
 

 true

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

This article is contributed by Aarti_Rathi and Pramod Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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