arithmetic - Exercise: Construct two numbers using figures 4,5 and 6 whose product is as big as possible

Precisely what it says in the title.

Construct two numbers using figures 4,5 and 6 whose product is as big as possible.

I don't know whether I can use a same number again (4456, f.e.) or only 4,5 and 6 (I'm guessing it's this one).

I could go about it with trial and error, but would like to know the reasoning behind it.

PS: I thought about 654 * 645 because the bigger the number in the place of the hundreds, the bigger the result.

Answer

There are only 6 choices, namely

$$6\times 54 = 324$$
$$6\times 45 = 270$$

$$5\times 64 = 320$$
$$5\times 46 = 230$$

$$4\times 56 = 224$$

$$4\times 65= 260$$

Thus the maximum is $$6\times 54 = 324$$