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📰 Thus, product always divisible by \( 2^3 = 8 \), \( 3 \), \( 5 \), so by \( \text{lcm}(8,3,5) = 120 \).
📰 And since for the sequence 1,2,3,4,5: product is \( 120 \), which is exactly 120. So no larger fixed integer divides all such products.
📰 Therefore, the largest integer that must divide the product of any five consecutive integers is \( \boxed{120} \).
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