Chords written upon two consecutive degrees of the [diatonic] scale can have no tones in common.
All other chords [in the diatonic scale] have common tones.
As Woodruff describes, the tonic triad shares no common tones with either II and VII (consecutive to I), one common tone with IV and V (four and five degrees from I) each, and two common tones with III and VI (three and six degrees from I) each.
B. Marx (1795–1866), and earlier theorists emphasized "common-tone retention and smooth voice leading in... [their] treatment[s] of harmonic succession [chord progressions]" (Engebretson 2008, p. 109).
The example below shows a circle progression in C major, in which common tones are retained in the second voice (alto).