| Summary: | In this paper we perform a further investigation for <i>r</i>-gcd-sum and <i>r</i>-lcm-sum functions. By making use of the properties of generalization of Euler’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-function, Abel’s identity and elementary arguments, we derive asymptotic formulas for the average of the <i>r</i>-gcd-sum function, <i>r</i>-lcm-sum function and their generalizations. Moreover, we also study the sums of reciprocals of <i>r</i>-gcd and <i>r</i>-lcm.
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