Oracle-bone 共 showed two hands lifting a vessel in offering — the physical act of doing something jointly. Twenty hands make light work; two hands make 共.
一共 totals your bill ('altogether'), 公共 marks what everyone shares, 共同 means mutual. The 共 in 共产党 (Communist Party) is this same 'together' — the character does groceries and geopolitics with equal ease.
Two hands lifting one thing — TOGETHER, ALTOGETHER.
When the waiter totals your table, the question is 一共多少? 'altogether how much?' — 共 is the last character you hear before every bill in China.