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Solution: We are to count how many integers from 1 to 120 are relatively prime to 12. This is given by Euler’s totient function applied to the set of positions, but since the condition is relative primality with 12, we compute $ \phi(12) $, the number of integers from 1 to 12 that are coprime to 12, and then multiply by the number of full cycles in 120.
First, factor 12:
$ 12 = 2^2 imes 3 $.

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