Find the LCM using Loops in C

To find the Least Common Multiple (LCM) of two numbers in C, we use loops to check for the smallest number that is evenly divisible by both numbers. The most common approach is using a loop to increment the maximum of the two numbers until we find a common multiple.

Examples of Finding LCM Using Loops

1. Finding LCM Using a while Loop

In this example, we use a while loop to iterate and find the smallest multiple of the two numbers.

main.c

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#include <stdio.h>

int main() {
    int num1, num2, lcm;

    // Input two numbers
    printf("Enter two numbers: ");
    scanf("%d %d", &num1, &num2);

    // Initialize LCM with the maximum of num1 and num2
    lcm = (num1 > num2) ? num1 : num2;

    // Loop to find the LCM
    while (1) {
        if (lcm % num1 == 0 && lcm % num2 == 0) {
            printf("LCM of %d and %d is %d\n", num1, num2, lcm);
            break;
        }
        lcm++; // Increment LCM value
    }

    return 0;
}

Explanation:

  1. We declare variables num1, num2 for input and lcm to store the result.
  2. We take input values for num1 and num2 using scanf().
  3. The variable lcm is initialized with the greater of the two numbers.
  4. A while loop is used to continuously check if lcm is divisible by both numbers.
  5. Once we find the LCM, we print it and use break to exit the loop.

Output:

Enter two numbers: 4 6
LCM of 4 and 6 is 12

2. Finding LCM Using a for Loop

In this example, we use a for loop to iterate through numbers starting from the maximum of the two numbers.

main.c

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#include <stdio.h>

int main() {
    int num1, num2, lcm, max;

    // Input two numbers
    printf("Enter two numbers: ");
    scanf("%d %d", &num1, &num2);

    // Get the maximum of the two numbers
    max = (num1 > num2) ? num1 : num2;

    // Finding LCM using a for loop
    for (lcm = max; ; lcm += max) {
        if (lcm % num1 == 0 && lcm % num2 == 0) {
            printf("LCM of %d and %d is %d\n", num1, num2, lcm);
            break;
        }
    }

    return 0;
}

Explanation:

  1. We declare variables num1, num2, lcm, and max.
  2. We take user input for num1 and num2 using scanf().
  3. The variable max stores the greater of the two numbers.
  4. A for loop starts at max and increments in steps of max.
  5. The loop breaks when we find the LCM, which is printed.

Output:

Enter two numbers: 5 10
LCM of 5 and 10 is 10

3. Finding LCM Using the GCD Formula

In this example, we calculate LCM using the formula: LCM(a, b) = (a * b) / GCD(a, b). We use a loop to find the Greatest Common Divisor (GCD) first.

main.c

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#include <stdio.h>

int main() {
    int num1, num2, gcd, lcm, i;

    // Input two numbers
    printf("Enter two numbers: ");
    scanf("%d %d", &num1, &num2);

    // Finding GCD using a loop
    for (i = 1; i <= num1 && i <= num2; i++) {
        if (num1 % i == 0 && num2 % i == 0) {
            gcd = i;
        }
    }

    // Using LCM formula
    lcm = (num1 * num2) / gcd;
    printf("LCM of %d and %d is %d\n", num1, num2, lcm);

    return 0;
}

Explanation:

  1. We declare variables for num1, num2, gcd, lcm, and an iterator i.
  2. We use a for loop to find the greatest common divisor (GCD) of the two numbers.
  3. We compute LCM using the formula (num1 * num2) / gcd.
  4. The result is printed.

Output:

Enter two numbers: 8 12
LCM of 8 and 12 is 24