Summary: Let \(n\geq1\) and \(k\geq0\) be integers with \(n\geq k\). Let \(C(n,k)\) denote the binomial coefficient indexed by \(n\) and \(k\), i.e. \(C(n,k)=\frac{n\times(n-1)\times\dots\times(n-k+1)} {1\times2\times\dots\times k}\). Define the lcm-analog of binomial coefficient by \(L(n,k)\frac{\mathrm {lcm}(n,n-1,\dots,n-k+1)} {\mathrm {lcm}(1,2,\dots,k)}\). In this paper, we prove that \(L(n,n-k)\) divides \(L(n,k)\) if \(k\leq\frac n2\), and give some couples \((n,k)\) satisfying that \(L(n,k)=L(n,n-k)\). Subsequently, we give a sufficient condition such that \(L(n,k)\) divides \(L(n+1,k)\). Finally, we provide a new proof for the known fact that \(L(n,k)\) divides \(C(n,k)\), and present many couples \((n,k)\) such that \(L(n,k)=C(n,k)\).