The main purpose of this paper is using the elementary and analytic methods to study the average variance mean value problem involving the F. Smarandache LCM function SL(n) and a number theory function SM(n),and give a sharper asymptotic formula for it.% 利用初等以及解析的方法研究Smarandache LCM函数SL（n）与数论函数SM（n）的均方差均值分布问题，并给出一个较强的渐近公式。
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