Source: https://guthlabs.ai/docs/instruments/gcd-lcm-calculator/implementation/

instrument implementation / implementation-contract

# GCD/LCM Calculator implementation

A source-bound implementation contract for GCD/LCM Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-057

**Effect**: Computation or source lookup only

## Input and validation requirements

- 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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gcd-lcm-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/gcd-lcm-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gcd-lcm-calculator/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`