  We give common generalizations of the Menon-type identities by
Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities
involve arithmetic functions of several variables, and also contain, as special
cases, identities for gcd-sum type functions. We point out a new Menon-type
identity concerning the lcm function. We present a simple character free
approach for the proof.
