CVP verified calculation capability

Least common multiple Calculation Capability

Exact LCM of two or more integers via BigInt pairwise GCF-identity fold, with listing and prime independent checks when values are small enough to list.

Math Capability ID math.lcm version 1.0.3 CVP VERIFIED CURRENT Core

Model

Via GCF

Via GCF: LCM(a,b) = |a / GCF(a,b) × b|
Pairwise: LCM(a,b,c,…) = LCM(LCM(a,b),c,…)
With zero: If any input is 0, LCM = 0
Primes: Take each prime to the highest power appearing in any factorization

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`values`	Two or more integers	—	input / output
`numbers`	Alias for values	—	input
`numsInput`	Share-URL / form field: comma- or space-separated integers	—	input
`value`	LCM: positive when every input is nonzero; 0 if any input is 0	—	output
`count`	—	—	output
`binary_formula`	—	—	output
`methods`	—	—	output
`work`	—	—	output
`max_digits`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	integer
`exactness`	exact
`algorithm`	lcm(a,b) = \|ab\| / gcd(a,b) extended to a list
`valid_domain`	integers
`singularity_policy`	not applicable — lcm(0, x) follows the published integer identity
`branch_policy`	not applicable — integer domain
`tolerance`	not applicable — exact integer identity
`convergence`	not applicable — non-iterative Euclidean / combinatorial
`conditioning`	not applicable — not a floating matrix
`rounding`	none — BigInt / exact integer
`overflow`	coded error or stringified BigInt when exceeding JSON number
`reproducibility`	deterministic exact integer + Capability@Version
`independent_oracle`	Evidence published cases
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Integer inputs; negatives treated by absolute value.
If any input is 0, LCM = 0. LCM(0,0)=0 is a CalculatorX/Python convention, not a GCF-identity derivation.
For nonzero inputs the result is a positive integer.

Example

One numerical check. The calculator page holds worked steps and FAQ.

LCM(8,12)=24; LCM(0,5)=0; LCM(9007199254740993, 3)=9007199254740993

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
Assurance: Core
Declared partition coverage: PASS · 8/8 declared partitions (lcm, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain)
Calculation version: 1.0.3
Verification: 20/20 calculation tests · 6/6 legacy golden · 7/7 legacy boundary · 7/7 legacy property
Production surface contract: 5/5
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 3/3 property · digest 243e5df78591
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 6/6 golden · 7/7 CVP boundary · 3/3 invalid · 3/3 property · 1/1 metamorphic · 1/1 cross-interface · 5/5 cross-calculator · 3/3 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.3 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.3 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/lcm' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"values":[8,12]},"calculation_version":"1.0.3"}'

{
  "inputs": {
    "values": [
      8,
      12
    ]
  },
  "calculation_version": "1.0.3"
}

POST /api/v1/calc/lcm. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: lcm
Engine: lcm
REST: POST /api/v1/calc/lcm
MCP: execute_calculation with capability_id: "math.lcm"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.3)
Versioned output schema: Immutable pin (1.0.3)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Derived identities

CalculatorX integer convention — Absolute value; 48-digit BigInt domain; divide-first identity

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.lcm"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.lcm","inputs":{"values":[8,12]},"calculation_version":"1.0.3"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.3) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.