We study in this paper bright late-type giants found in the First Byurakan Survey (FBS) data base. Phase dependent light-curves from large sky area variability data bases such as Catalina Sky Survey (CSS) and All-Sky Automated Survey for Supernovae (ASAS-SN), and the early installment of the third Gaia data release (Gaia EDR3) photometric and astrometric data have been used to characterize our sample of 1 100 M-type giants and 130 C-type stars found at high latitudes. Gaia radial velocities (RV) are available for 134 and luminosities for 158 stars out of 1 100. We show the behaviour of our sample stars in a Gaia color–absolute magnitude diagram (CaMD), the Gaia-2MASS-diagram from Lebzelter et al. with some alternative versions. In this way we explore the potential of these diagrams and their combination for the analysis and interpretation of datasets of LPVs. We show the possibility to classify stars into M- and C-types and to identify the mass of the bulk of the sample stars.