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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _common_rational_period(rational_periods: List[fractions.Fraction] ) -> fractions.Fraction: """Finds the least common integer multiple of some fractions. The solution is the smallest positive integer c such that there exists integers n_k satisfying p_k * n_k = c for all k. """

    assert rational_periods, "no well-defined solution for an empty list"
    common_denom = _lcm(p.denominator for p in rational_periods)
    int_periods = [p.numerator * common_denom // p.denominator
                   for p in rational_periods]
    int_common_period = _lcm(int_periods)
    return fractions.Fraction(int_common_period, common_denom)