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The least common multiple (LCM) of two numbers is defined as the smallest positive integer that is a multiple of both numbers. Choosing the smallest product that is a multiple of both reflects this definition accurately.

For example, if we consider the numbers 4 and 5, their multiples are 4, 8, 12, 16, 20, and 5, 10, 15, 20. The smallest number that appears in both sequences is 20, confirming that the LCM is indeed 20. Therefore, this option rightly captures the concept of LCM by identifying it as the smallest shared multiple of the two numbers involved.