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  "api": "https://www.calculatorx.com/api/v1/calc/lcm",
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  "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."
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    "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."
  ],
  "boundary_conditions": [
    "Need at least two numbers → NEED_TWO_NUMBERS",
    "Missing list → MISSING_REQUIRED_INPUT",
    "Non-integers rejected → INVALID_NUMBER",
    "More than 48 digits → VALUE_ABOVE_MAX",
    "Any zero → LCM = 0"
  ],
  "sources": [
    {
      "title": "Encyclopedia of Mathematics — Least common multiple",
      "section": "Definition; pairwise fold; relation to GCD",
      "url": "https://encyclopediaofmath.org/wiki/Least_common_multiple",
      "supports": "LCM of n integers via pairwise fold; lcm(a,b)·gcd(a,b)=|ab| for nonzero a,b",
      "kind": "reference"
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      "section": "If any argument is zero, LCM = 0",
      "url": "https://docs.python.org/3/library/math.html#math.lcm",
      "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)",
      "kind": "reference"
    },
    {
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      "section": "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|",
      "kind": "definition"
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    {
      "title": "MIT Mathematics for Computer Science — Chapter 8: Number Theory",
      "section": "Chapter 8, including sections 8.2–8.9 and problem 8.24",
      "url": "https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/mit6_042js15_textbook.pdf",
      "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.",
      "kind": "reference",
      "publisher": "Massachusetts Institute of Technology"
    }
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  "methods": [
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    "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)"
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