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Each sandwich needs 2 slices of bread and 1 slice of cheese. You have 10 slices of bread and 8 slices of cheese. How many sandwiches? Bread allows 5; cheese allows 8. You can only make 5 — the bread runs out first.
Reactions are identical. Whichever reactant runs out first stops the reaction. That one is the limiting reactant, and it sets the maximum product.