// multi-utility computation suite · offline · instant · precise
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│ [c] calcalyst_ │
│ computation suite │
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math.number-theory-gcd Calculator
Computes GCD using the Euclidean algorithm with full step-by-step trace, finds Bézout coefficients, and checks coprimality. Bézout's identity guarantees that ax + by = gcd(a,b) always has integer solutions — the extended Euclidean algorithm finds them.
Inputs
A
Reference formula or conversion factor shown for context.
B
Reference formula or conversion factor shown for context.
C
Reference formula or conversion factor shown for context.
Results
GCD(a,b)
GCD (greatest common divisor) -- the largest integer that divides both numbers with no remainder. Used in fraction simplification and modular arithmetic.
LCM(a,b)
LCM (least common multiple) -- the smallest number divisible by both inputs. Used when finding common denominators.
GCD(a,b,c)
GCD (greatest common divisor) -- the largest integer that divides both numbers with no remainder. Used in fraction simplification and modular arithmetic.
LCM(a,b,c)
LCM (least common multiple) -- the smallest number divisible by both inputs. Used when finding common denominators.
coprime?
Reference formula or conversion factor shown for context.
Euclidean algorithm
The selected or recommended algorithm for this problem type based on the inputs.