Let $a,b$ and n be positive integers and let $S=\{x_1, \ldots , x_n\}$ be a set of n distinct positive integers. For ${x\in S}$ , define $G_{S}(x)=\{d\in S: d. Denote by $[S^a]$ the $n\times n$ matrix having the a th power of the least common multiple of $x_i$ and $x_j$ as its $(i,j)$ -entry. We show that the b th power matrix $[S^b]$ is divisible by the a th power matrix $[S^a]$ if $a\mid b$ and S is gcd closed (that is, $\gcd (x_i, x_j)\in S$ for all integers i and j with $1\le i, j\le n$) and $\max _{x\in S} \{|G_S (x)|\}=1$. This confirms a conjecture of Shaofang Hong ['Divisibility properties of power GCD matrices and power LCM matrices', Linear Algebra Appl. 428 (2008), 1001–1008]. [ABSTRACT FROM AUTHOR]