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GCD and LCM Calculator
Enter two positive integers — the calculator returns GCD and LCM using the Euclidean algorithm.
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How we calculate
GCD uses the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b). LCM = |a × b| / GCD(a, b).
Example: GCD(12, 8)
GCD(12, 8) = 4. LCM(12, 8) = 12×8/4 = 24.
Frequently asked questions
What is GCD?
Greatest Common Divisor — the largest integer that divides both numbers without a remainder.
What is LCM?
Least Common Multiple — the smallest positive integer that is divisible by both numbers.
How is GCD used in fractions?
GCD is used to simplify fractions: divide both numerator and denominator by GCD.
How is LCM used in fractions?
LCM gives the common denominator needed for adding or subtracting fractions.
What is the Euclidean algorithm?
An efficient method: GCD(a,b) = GCD(b, a mod b). Repeat until b=0, then a is the GCD.
What if GCD equals 1?
If GCD(a,b) = 1, the numbers are coprime (no common factors except 1).
Can GCD be used with more than 2 numbers?
Yes: GCD(a,b,c) = GCD(GCD(a,b), c). Apply iteratively.
Is LCM always larger than both numbers?
Yes, unless one number is a multiple of the other — then LCM equals the larger number.
What if one number is zero?
By convention, GCD(0, n) = n. LCM(0, n) = 0.
What are coprime numbers?
Two numbers are coprime if their GCD equals 1. Example: 8 and 15 (GCD=1).
For educational purposes.