Multiply large numbers

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Consider the product $723145878987 \times599987871$.

If I want to know that what would be sum of unit and tens digit of the result then Is there a trick that I could find it as fastly as possible?

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The sum of the unit and tens digit of that product is the same as for $87 \times 71$ (the last two digits of each number). All of the more significant digits are irrelevant. (Start doing the multiplication by hand using the traditional multiplication algorithm taught in school, and you will see why.)