What you have to realize is who is creating the charge and who is receiving it.
Oxygen and Aluminum are in their ionic form. Ions are produced by electron movement.
Aluminum gives away electrons (3 of them).
Oxygen takes on electrons (2 of them).
The 2 and the 3 in Al2O3 tells you how many electrons were given up and how they were taken on.
The 2 and the 3 in Al2O3 also tells you (indirectly) what the lowest common denominator is.
So once you understand the above 2 sentences you will understand the answer to your questions.
The lowest common multiple of 3 and 2 is six.
If the Aluminum gives up 3 electrons per atom, then to get to 6, you will have to have two aluminums.
If oxygen takes on 2 electrons then to get to six. There must be 3 oxygens present. Look at the formula
Al2 there are two aluminums
O3 there are three oxygens. That's why the formula is written the way it is.
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Aluminum is never seen alone because it is very eager to give up it's 3 electrons. It will combine with almost anything that is willing to receive those electrons.
Compare it to gold. Gold will combine with almost nothing ionically. Separating gold from a none metal won't happen normally, and refining to get rid of that problem just won't occur.
