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To find the smallest positive whole number that, when multiplied by 180, results in a multiple of 100, we need to determine the least common multiple (LCM) of 180 and 100. The prime factorization of 180 is (2^2 \times 3^2 \times 5) and for 100, it is (2^2 \times 5^2). The LCM requires the highest powers of each prime: (2^2), (3^2), and (5^2), which gives us 900. Therefore, dividing 900 by 180 gives us 5. Thus, the smallest positive whole number is 5.

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