This content originally appeared on DEV Community and was authored by Mohammed mhanna
Numbers hide patterns that are incredibly useful in programming, math, and real-world applications. Two of these fundamental concepts are GCD (Greatest Common Divisor) and LCM (Least Common Multiple).
Before we dive into Java, let’s understand what they are and why they matter.
🔹 1. What Are GCD & LCM?
GCD (Greatest Common Divisor): The largest number that divides two integers without leaving a remainder.
Example: GCD(12, 18) = 6
LCM (Least Common Multiple): The smallest number that is a multiple of two integers.
Example: LCM(12, 18) = 36
đź’ˇ Relationship:
LCM(a , b) Ă— GCD(a , b) = a Ă— b
🔹 2. Why Do We Use Them?
Simplifying fractions → Use GCD to reduce fractions to lowest terms.
Scheduling problems → LCM helps find repeating cycles or alignments.
Mathematical algorithms → Many coding challenges use GCD and LCM.
Optimizing computations → Finding GCD efficiently can reduce problem complexity.
🔹 3. Pseudo-Code:
3.1 GCD (Euclidean Algorithm):
function GCD(a, b):
while b ≠0:
temp = b
b = a mod b
a = temp
return a
3.2 LCM Using GCD
function LCM(a, b):
return (a * b) / GCD(a, b)
đź’ˇ Tip: Always calculate GCD first to make LCM computation safe and efficient.
🔹 4. Java Implementation
4.1 GCD in Java
public static int gcd(int a, int b) {
while (b != 0) {
int temp = b;
b = a % b;
a = temp;
}
return a;
}
4.2 LCM in Java
public static int lcm(int a, int b) {
return (a * b) / gcd(a, b);
}
4.3 Test the Methods
public static void main(String[] args) {
int num1 = 12;
int num2 = 18;
System.out.println("GCD: " + gcd(num1, num2)); // 6
System.out.println("LCM: " + lcm(num1, num2)); // 36
}
🔹 5. Real-World Examples
Simplifying fractions: 18/24 → divide numerator and denominator by GCD(18,24)=6 → 3/4
Task scheduling: Two tasks repeat every 12 and 18 days → they align every LCM(12,18)=36 days
Coding challenges: Problems often require finding co-prime numbers or least common multiples
🎯 Key Takeaways
GCD is the largest factor, LCM is the smallest multiple.
Euclidean Algorithm is efficient and widely used.
LCM can always be derived from GCD.
These concepts are foundational for math-heavy programming and algorithms.
đź’¬ Question:
Have you ever solved a real-world problem using GCD or LCM? Share your example!
This content originally appeared on DEV Community and was authored by Mohammed mhanna
Mohammed mhanna | Sciencx (2025-10-01T14:44:50+00:00) 🔢 GCD & LCM. Retrieved from https://www.scien.cx/2025/10/01/%f0%9f%94%a2-gcd-lcm/
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