查找两个质数的LCM的程序

给定两个质数N和M ，任务是找到两个给定质数的最小公倍数(LCM)。
例子：

Input: N = 3, M = 7 
Output: 21 
Explanation: 
The least numbers greater than equals to 3 and 7 which is a multiple of 3 and 7 is 21.

Input: N = 5, M = 5 
Output: 5 
Explanation: 
The least numbers greater than equals to 5 and 5 which is a multiple of 5 and 5 is 5. 
 

方法：我们知道两个数的乘积等于它们的最大公除数(GCD)和最小公倍数(LCM)的乘积。因此，两个给定质数的LCM可以由下式给出： $LCM(a, b) = \frac{a * b}{GCD(a, b)}$ 。
由于GCD两个不同的质数为1，因此$LCM(a, b) = a * b$ ，如果两个给定的数字相同，则LCM就是数字本身。

下面是上述方法的实现：

C++

// C++ Program to find LCM of two
// prime numbers
#include 
using namespace std;
 
// Function to return the LCM of two
// prime numbers
int findLCMPrime(int a, int b)
{
    // If the two numbers are equal
    // then return any one of a and b
    if (a == b) {
        return a;
    }
 
    // Else return product of numbers
    return a * b;
}
 
// Driver code
int main()
{
    // Given two numbers
    int a = 3, b = 5;
 
    // Function Call
    cout << findLCMPrime(a, b);
    return 0;
}

Java

// Java Program to find LCM of two
// prime numbers
class GFG{
     
// Function to return the LCM of two
// prime numbers
static int findLCMPrime(int a, int b)
{
    // If the two numbers are equal
    // then return any one of a and b
    if (a == b)
    {
        return a;
    }
 
    // Else return product of numbers
    return a * b;
}
 
// Driver code
public static void main (String[] args)
{
    // Given two numbers
    int a = 3, b = 5;
 
    // Function Call
    System.out.println(findLCMPrime(a, b));
}
}
 
// This code is contributed by AnkitRai01

Python3

# Python3 program to find LCM of two
# prime numbers
 
# Function to return the LCM of two
# prime numbers
def findLCMPrime(a, b):
 
    # If the two numbers are equal
    # then return any one of a and b
    if (a == b):
        return a;
 
    # Else return product of the numbers
    return a * b;
 
# Driver code
if __name__ == "__main__":
 
    # Given two numbers
    a = 3; b = 5;
 
    # Function Call
    print(findLCMPrime(a, b));
 
# This code is contributed by AnkitRai01

C#

// C# program to find LCM of two prime numbers
using System;
 
class GFG{
     
// Function to return the LCM of two
// prime numbers
static int findLCMPrime(int a, int b)
{
     
    // If the two numbers are equal
    // then return any one of a and b
    if (a == b)
    {
        return a;
    }
     
    // Else return product of numbers
    return a * b;
}
     
// Driver code
public static void Main (string[] args)
{
     
    // Given two numbers
    int a = 3, b = 5;
     
    // Function Call
    Console.WriteLine(findLCMPrime(a, b));
}
}
 
// This code is contributed by AnkitRai01

Javascript

 
// Javascript Program to find LCM of two
// prime numbers
 
// Function to return the LCM of two
// prime numbers
function findLCMPrime(a, b)
{
     
    // If the two numbers are equal
    // then return any one of a and b
    if (a == b)
    {
        return a;
    }
   
    // Else return product of numbers
    return a * b;
}
  
// Driver code
 
// Given two numbers
let a = 3, b = 5;
 
// Function Call
document.write(findLCMPrime(a, b));
  
// This code is contributed by Akshit Saxena
  

输出

15

时间复杂度： O(1)