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Modular C Program: GCD & LCM

GCD & LCM using Functions

Presented by : Prajwal S Metri

Problem Definition

Develop a modular C program to calculate the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) for two integers, using a separate function.

A digital illustration of mathematical symbols and C programming code floating in a structured abstract digital space, cyan and blue colors

Mathematical Logic

The Euclidean algorithm is efficient for GCD. It states: GCD(a, b) = GCD(b, a % b) until b becomes 0. The GCD is then 'a'. LCM is calculated as: (a × b) / GCD(a, b).

Diagram illustrating the Euclidean algorithm with geometric rectangles being subdivided, educational vector art style, blue and cyan tones

Algorithm Process

Step 1: Define separate functions for GCD and LCM logic.
Step 2: In main(), input numbers and call the functions.
Step 3: Print the returned values from gcd() and lcm().

C Program Implementation

#include 

int gcd(int a, int b) {
    while (b != 0) {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}
int lcm(int a, int b) {
    if (a==0 || b==0) return 0;
    return (a * b) / gcd(a, b);
}
int main() {
    int n1 = 12, n2 = 18;
    printf("GCD: %d\n", gcd(n1, n2));
    printf("LCM: %d\n", lcm(n1, n2));
    return 0;
}

Program Output Examples

Example 1

Input: 12, 18\nGCD: 6\nLCM: 36

Example 2

Input: 10, 25\nGCD: 5\nLCM: 50

Summary & Key Takeaways

✔ Efficient implementation of Euclidean algorithm.
✔ Modular programming improves code cleanliness and reusability.
✔ LCM is derived directly from the GCD relationship.

Thank You

Modular C Program: GCD & LCM

GCD & LCM using Functions

Presented by : Prajwal S Metri

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