LCM & GCD Calculator

Frequently Asked Questions

What is the difference between LCM and GCD?

GCD (greatest common divisor) is the largest number dividing both. LCM (least common multiple) is the smallest number both divide. For 12 and 18: GCD = 6, LCM = 36.

How are LCM and GCD related?

For any two positive integers: LCM(a, b) × GCD(a, b) = a × b. Once you know one, the other is easy.

How do I find GCD by hand?

Use the Euclidean algorithm: divide, take remainder, repeat. GCD(48, 18) → 48 mod 18 = 12 → 18 mod 12 = 6 → 12 mod 6 = 0 → GCD = 6.

When do I need LCM in real life?

When adding fractions with different denominators, scheduling repeating events, or determining when two cycles align.

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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Enter two or more positive integers separated by commas, spaces, or semicolons. The calculator splits your text into numbers, discards anything that is not a positive integer, then finds the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM). It uses the Euclidean algorithm for the GCD and extends to any count of inputs by chaining the operation pairwise - gcd(a, b, c) = gcd(gcd(a, b), c).

Formula

The Euclidean algorithm computes gcd(a, b) = gcd(b, a mod b), repeating until the remainder is zero; the last nonzero value is the GCD. The LCM follows directly: LCM(a, b) = |a × b| ÷ GCD(a, b). For more than two numbers the tool folds these formulas across the whole list, so GCD divides every input and LCM is divisible by every input.

Common Mistakes

Entering only one number - the tool needs at least two integers to compare.

Including zero or negative values; only positive integers are counted.

Confusing GCD with LCM - GCD is never larger than your smallest input, while LCM is never smaller than your largest.

Using decimals or fractions; this tool works only on whole numbers.

Tips & FAQ

How do I simplify a fraction? Divide numerator and denominator by their GCD. 24/36 ÷ GCD(24,36)=12 gives 2/3.

What is the LCD? The Least Common Denominator is just the LCM of the denominators. To add 1/4 + 1/6, LCD = LCM(4,6) = 12.

Is GCD the same as HCF? Yes - Highest Common Factor (HCF) is another name for the Greatest Common Divisor.

LCM & GCD Calculator

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