GCD & LCM Calculator

The Greatest Common Divisor (GCD) — also called the Greatest Common Factor (GCF) or Highest Common Factor (HCF) — is the largest positive integer that divides all given numbers without a remainder. For example, the GCD of 48 and 18 is 6, because 6 is the largest number that divides both evenly. The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers. The LCM of 48 and 18 is 144. GCD and LCM are fundamentally linked by the relationship GCD(a, b) × LCM(a, b) = a × bfor any two positive integers. Our GCD & LCM calculator uses this relationship and the Euclidean algorithm to compute both values accurately for any set of numbers.

1. 1. Enter Your Numbers: Type two or more positive integers separated by commas or spaces. The GCD & LCM calculator accepts any integers from 1 to 1,000,000,000. All processing happens locally in your browser — your data never leaves your device.
2. 2. Instant Calculation: Click "Calculate GCD & LCM" and the tool instantly computes the GCD using the Euclidean algorithm and the LCM using the GCD relationship. For two-number inputs, a full step-by-step Euclidean algorithm table is shown.
3. 3. Review Results: View the GCD and LCM values, prime factorizations for each input number, and a divisibility verification table confirming the results are correct.

• Euclidean Algorithm (GCD): The most efficient method for computing GCD. Repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is 0. The last non-zero remainder is the GCD. For example: GCD(48, 18) → 48 = 2×18 + 12 → 18 = 1×12 + 6 → 12 = 2×6 + 0 → GCD = 6.
• LCM via GCD: LCM(a, b) = |a × b| ÷ GCD(a, b). This avoids computing prime factorizations and is efficient for large numbers. For multiple numbers, the GCD and LCM are computed iteratively: GCD(a, b, c) = GCD(GCD(a, b), c).
• Prime Factorization Method: The GCD takes the minimum exponent of each shared prime factor; the LCM takes the maximum exponent of each prime factor across all numbers. Our calculator displays the prime factorization of each input for educational reference.
• Coprime Numbers: Two numbers are coprime (relatively prime) when their GCD equals 1. In this case, their LCM equals their product. Our GCD & LCM calculator identifies coprime pairs automatically.

The GCD is used when you need to reduce or divide — simplifying fractions, finding the largest common tile size, or splitting items into equal groups. The LCM is used when you need to combine or synchronize — finding common denominators, scheduling repeating events, or determining when cycles align. Both values are always positive integers, and for any two numbers a and b, GCD(a, b) always divides LCM(a, b).