GCD/LCM Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-4

Evidence ID

t4-057

Ledger rows

1

No ledger note is attached.

Review findings

Core Euclidean and extended-Euclidean methods are mathematically correct, but the specification is not complete enough for an unambiguous production instrument. The honest label should state accepted cardinality, integer-only validation, sign conventions, zero conventions, and how coefficients are returned for 2+ inputs.

Formula and scope findings

• The stated Euclidean algorithm correctly supports GCD computation, and the extended Euclidean algorithm correctly supports Bezout coefficients.
• The LCM formula is not explicitly specified. For two integers, use lcm(a,b)=|ab|/gcd(a,b), with a zero-result convention; for multiple integers, apply lcm iteratively or define an equivalent general rule.
• For 2+ integers, the meaning and ordering of multiple Bezout coefficients is not explicitly defined; they should satisfy a1*c1+...+an*cn=GCD(a1,...,an).

Unit assumptions

• All inputs are mathematical integers with no physical units.
• GCD is assumed to be the nonnegative greatest common divisor, including gcd(0,n)=|n|.
• LCM is assumed to be nonnegative, including lcm(0,n)=0 and lcm(0,0)=0 if all inputs are zero.
• For multiple inputs, Bezout coefficients correspond positionally to the input list and satisfy the linear combination equal to the positive GCD.

Boundary hardening

Recorded hazards

• Division by zero must be prevented when implementing lcm(a,b)=|ab|/gcd(a,b); the all-zero case requires an explicit convention.
• An empty input list is invalid and must be rejected because GCD, LCM, and Bezout coefficients are undefined without an agreed empty-list convention.
• A single integer conflicts with the stated 2+ input requirement and should be rejected or explicitly supported.
• Inputs must be validated as integers; fractional, NaN, infinity, and nonnumeric values are invalid.
• For multiple integers, naive multiplication can overflow fixed-width numeric types; arbitrary-precision integers or overflow-safe arithmetic may be required.
• Negative-input behavior must be specified, especially the sign of GCD and LCM and the nonuniqueness of Bezout coefficients.
• The all-zero input list needs an explicit policy: gcd(0,...,0) is commonly defined as 0, while Bezout coefficients are nonunique and the LCM convention varies.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "integers": [
      84,
      30
    ]
  },
  "expected_outputs": {
    "gcd": 6,
    "lcm": 420,
    "bezout_coefficients": [
      -1,
      3
    ]
  },
  "working": "84 = 2*30 + 24; 30 = 1*24 + 6; therefore gcd = 6. Back-substitute: 6 = 30 - 24 = 30 - (84 - 2*30) = -1*84 + 3*30, so coefficients are [-1,3]. lcm = |84*30|/6 = 2520/6 = 420."
}

Related workflows

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche4/tranche4-results.json