Another way to practice this technique is by adding another note to the LH. The scale degrees will be 1-5-1-2-3:
LH/RH
C major: C, G, C, D, E / G-C-E
C minor: C, G, C, D, Eb / G-C-Eb
C diminished (dim7): C, Gb, C, D, Eb / Gb-(A)-C-Eb
C augmented: C, G#, C, D, E / G#-C-E