Public evidence

math.lcm

Machine-checked verification for calculation version 1.0.4 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

2–32 signed integers,48 digits each, strict matching aliases, complete exact result/work; any zero→0; bounded listing and prime checks

Declared partition coverage: PASS · 8/8 declared partitions (lcm, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain)
Versions: Calculation 1.0.4 · CVP protocol 1.0.0-proposed · Evidence 2026-10-21.lcm-complete-contract-v2
Verification revision: 2026-10-21.lcm-complete-contract-v2 · 3/3 property · digest f87d285d6b3e

Verification

Legacy regression suite: 20/20 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (20/20 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-21.lcm-complete-contract-v2. Calculation version 1.0.4. CVP 1.0.0-proposed. 9/9 golden · 7/7 CVP boundary · 3/3 invalid · 3/3 property · 1/1 metamorphic · 1/1 cross-interface · 5/5 cross-calculator · 6/6 CVP contract. digest f87d285d6b3e.

Golden (oracle-backed) 9 / 9
CVP boundary 7 / 7
Invalid input 3 / 3
Property 3 / 3
Metamorphic 1 / 1
Cross-interface 1 / 1
Cross-calculator 5 / 5
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Core

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:54e7f3e7c20bd5278c8d04377ee0b049889e093b2cc978e56e7b8c1bf5bd7168

Input schema sha256:5374ad9a3a62305c7a5982e9b2d82f2c0135d3fc1bed99a6a31cf35b9652afc9 · Output schema sha256:ba4aed58d4673eee1b77ab2ad6d7920f38f350bf710369ec73c8dfda97b3c87a · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: lcm
Engine: lcm
Engine build: 2026-10-21
Evidence core: 2026-10-21T03:41:55.953Z
Rendered: 2026-10-22T04:36:23.763Z
Last reviewed: —

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.

Limitations

Exact relative to accepted normalized integers; cannot recover precision already lost by the client or JSON numeric parsing.
2–32 values,48 decimal digits per integer,4096 list characters; matching ordered aliases required.
Listing bound5000 and inputs≤500, at most80 displayed multiples per row with explicit omission; prime cross-check input bound1000000.
Result may contain up to1536 decimal digits; summary/full and exports preserve the complete integer.

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Encyclopedia of Mathematics — Least common multiple — Definition; pairwise fold; relation to GCD
Supports: LCM of n integers via pairwise fold; lcm(a,b)·gcd(a,b)=|ab| for nonzero a,b
Python math.lcm — zero convention — If any argument is zero, LCM = 0
Supports: Any zero argument → 0; LCM(0,0)=0 is that convention, not |a/GCF(a,b)×b| (Python separately defines gcd(0,0)=0; the division identity is not used here)
CalculatorX integer convention — Absolute value; 48-digit BigInt domain; divide-first identity
Supports: Negatives by |n|; exact BigInt with a product digit cap; LCM(a,b)=|a/GCF(a,b)×b|
MIT Mathematics for Computer Science — Chapter 8: Number Theory — Chapter 8, including sections 8.2–8.9 and problem 8.24
Supports: Divisibility, prime factorization, gcd and the Euclidean algorithm, lcm via prime exponents, division with remainder, modular congruence and multiplicative inverses. CalculatorX’s signed-remainder and zero-input policies are stated separately on the page. Mathematical reference only; not validation or endorsement of this implementation.

Methods

Algorithms this engine uses. Not external references.

Pairwise GCF-identity fold (canonical engine; divide before multiply)
Prime-factor LCM (cross-check when every |n| ≤ 1,000,000 and none is 0)
Listing multiples (cross-check when LCM ≤ 5,000 and every |n| ≤ 500)

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.