Write a C++ program to calculate and display the Least Common Multiple of two given integers.
Input and Output Examples
Example 1:
- Input: 12, 18
Output: The LCM of 12 and 18 is 36.
Example 2:
- Input: 25, 15
Output: The LCM of 25 and 15 is 75.
Algorithm to Find LCM of two numbers
- Start the program.
- Prompt the user to enter two integers.
- Read the integers.
- Calculate the greatest common divisor (GCD) of the two numbers using the Euclidean algorithm.
- Calculate the LCM using the relationship between GCD and LCM, which is LCM(a,b)=GCD(a,b)∣a×b∣.
- Display the LCM.
- End the program.
Below is the C++ code for finding the LCM:
cpp
#include <iostream>
using namespace std;
// Function to compute the GCD of two numbers
int gcd(int a, int b) {
// Continue until the remainder is 0
while (b != 0) {
int remainder = a % b;
a = b;
b = remainder;
}
return a; // The GCD is the last non-zero remainder
}
// Main function to drive the program
int main() {
// Declare variables to store the two numbers
int num1, num2;
// Prompt the user for two numbers
cout << "Enter two numbers: ";
cin >> num1 >> num2;
// Calculate GCD
int gcdValue = gcd(num1, num2);
// Calculate LCM using the relationship between GCD and LCM
int lcm = (num1 * num2) / gcdValue;
// Display the LCM
cout << "The LCM of " << num1 << " and " << num2 << " is " << lcm << "." << endl;
// Ending the program
return 0;
}
Testing the Program with Different Input Values
- Input: 100, 40
- Output: The LCM of 100 and 40 is 200.
- Input: 7, 5
- Output: The LCM of 7 and 5 is 35.