{
  "abstract": "For $r \\ge 0$, let $\\mathcal P_r=\\{\\binom{r}{0},\\binom{r}{1},\\ldots,\\binom{r}{\\lfloor r/2\\rfloor}\\}$ be the set of distinct entries in row $r$ of Pascal's triangle. We study the least possible least common multiple of $n$ entries chosen from one row, with the row itself also free: $a(n)=\\min_{r\\ge0,\\ S\\subseteq\\mathcal P_r,\\ |S|=n}\\operatorname{lcm}(S)$. Whereas the least common multiple of an entire row is given by a classical identity of Farhi, allowing both the row and the selected coefficients to vary creates a different optimization problem. We first recast the fixed-row problem exactly as a weighted prime-power exclusion problem, which explains how omitting a few coefficients can remove expensive prime-power contributions. Our main asymptotic result is $\\log a(n)=2n+O\\!\\left(n\\exp\\!\\left(-c(\\log n)^{3/5}(\\log\\log n)^{-1/5}\\right)\\right)$ for some absolute $c>0$, so $a(n)^{1/n}\\to e^2$. A two-band refinement further shows that every optimal row satisfies $r_n=2n+O\\!\\left(n\\exp\\!\\left(-c(\\log n)^{3/5}(\\log\\log n)^{-1/5}\\right)\\right)$, and that the minimum prefix defect of an optimal support is $o(n)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23024",
  "author_total": 1,
  "authors": [
    {
      "name": "Felix Huber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e8gsc9j0a20w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23024",
  "fulltext_url": null,
  "id": "1e8gsc9j0a20w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23024",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214032663",
  "pdf_url": "https://arxiv.org/pdf/2609.23024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e8gsc9j0a20w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.23024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal Least Common Multiples in Rows of Pascal's Triangle",
  "title_text": "Extremal Least Common Multiples in Rows of Pascal's Triangle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/1e8gsc9j0a20w",
  "venue": "arXiv",
  "versions": []
}