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Claim. The answer is yes, in a strong form. Theorem 1 of S. Cambie, Resolution of an Erdős' problem on least common multiples, arXiv:2410.09138v1 (11 October 2024; the text dated October 15, 2024), 5 pages, states that for every constant $C\ge1$ and every sufficiently large $k$ there are integers $0<x<y$ with $y>x+k$ and

$$\operatorname{lcm}\{x,\ldots,x+k-1\}>C\cdot\operatorname{lcm}\{y,\ldots,y+k\}.$$

In the site's notation $M(n,k)=[n+1,\ldots,n+k]$, the substitution $n=x-1$, $m=y-1$ turns this into $M(n,k)>C\cdot M(m,k+1)$ with $m\ge n+k+1$, so for $C=1$ every sufficiently large $k$, and in particular infinitely many $k\ge3$, yields a triple $(m,n,k)$ with $m\ge n+k$ and $M(n,k)>M(m,k+1)$, which is what the problem asks; the ratio can moreover exceed any constant. The result page Theorem 1 on the source card cambie_2024_resolution_erdos_problem_least_common_multiples records the statement, the minimal examples $M(52,7)>M(62,8)$ and $M(36,8)>M(47,9)$, and the structure of the proof: Chinese-remainder families of $x$ and $y$ with prescribed residues modulo the primes in $(\sqrt k,k]$, the density of primes near $k/2$ and $k$, and a valuation identity comparing the two products with their least common multiples.

Acceptance. Reviewed: Thomas Bloom, the site's curator, rests the label PROVED (LEAN) on this paper. The commentary (page last edited 11 January 2026) credits the positive answer to Cambie in the strong form above, after a thread of 6 to 8 January 2026 in which the fixed-$k$ reading of the 1979 wording was refuted and the statement on the page was changed to the varying-$k$ question; the site's summary sentence calls the problem solved in the affirmative with the proof verified in Lean. Not refereed: the arXiv listing carries no journal reference, a Crossref bibliographic query for the title returned no record, and Semantic Scholar listed no citing paper on 2026-09-18, so the paper stands as a preprint; a refereed version would add refereed here. Read depth: the statements of Theorem 1, Conjecture 2, Question 3 and Claims 4 and 5 are checked, and the two-page proof only for its structure; nothing is independently reviewed by this project.

The Lean label. The site's "(Lean)" suffix is a catalog label. The thread comment of 8 January 2026 announced a Lean formalization of Theorem 1 by Aristotle, Harmonic's automated prover, conditional at that time on a prime number theorem statement declared as an axiom; the version linked above, the file src/latest/ErdosProblems/Erdos678.lean of Boris Alexeev's repository plby/lean-proofs at its commit of 1 August 2026, declares itself a formalization of the paper's first main result, naming Cambie as informal author and Aristotle and Alexeev as formal authors, so it is a link on this page and not a claim of its own; it derives the needed density hypothesis from an imported external Lean project instead of an axiom, and its end results include the site's statement, infinitely many triples, and the negations of the fixed-$k$ readings. The formal-conjectures statement file, described on the problem page, names that development in its formal_proof attributes and keeps a sorry body of its own; a statement file is not a formalization and is not linked here. This corpus did not build or kernel-check these files, the imported project's axioms were not examined, and no statement-fidelity review exists, so formalized is not listed and the label warrants no kernel credit.

Scope. Full. The paper's Conjecture 2 (a larger block with $C$ extra elements) and Question 3 (a Chinese-remainder density statement implying it) remain open per the paper and are not part of this claim. The fixed-$k$ reading of Erdős's 1979 sentence, false for every $k$, is a Formulation note on the problem page and not a question this claim answers.

Depends on. No page of this wiki. The proof is self-contained in the paper apart from the distribution of primes in short intervals, which it cites.