code: def _periodicity(args, symbol):
      """
      Helper for `periodicity` to find the period of a list of simpler
      functions.
      It uses the `lcim` method to find the least common period of
      all the functions.
  
      Parameters
      ==========
  
      args : Tuple of :py:class:`~.Symbol`
          All the symbols present in a function.
  
      symbol : :py:class:`~.Symbol`
          The symbol over which the function is to be evaluated.
  
      Returns
      =======
  
      period
          The least common period of the function for all the symbols
          of the function.
          ``None`` if for at least one of the symbols the function is aperiodic.
  
      """
      periods = []
      for f in args:
          period = periodicity(f, symbol)
          if period is None:
              return None
  
          if period is not S.Zero:
              periods.append(period)
  
      if len(periods) > 1:
          return lcim(periods)
  
      if periods:
          return periods[0]
  
imports: from .accumulationbounds import AccumBounds, AccumulationBounds
  from .singularities import singularities
  from sympy.core import Pow, S
  from sympy.core.function import diff, expand_mul, Function
  from sympy.core.kind import NumberKind
  from sympy.core.mod import Mod
  from sympy.core.numbers import equal_valued
  from sympy.core.relational import Relational
  from sympy.core.symbol import Symbol, Dummy
  from sympy.core.sympify import _sympify
  from sympy.functions.elementary.complexes import Abs, im, re
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.integers import frac
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.functions.elementary.trigonometric import TrigonometricFunction, sin, cos, tan, cot, csc, sec, asin, acos, acot, atan, asec, acsc
  from sympy.functions.elementary.hyperbolic import sinh, cosh, tanh, coth, sech, csch, asinh, acosh, atanh, acoth, asech, acsch
  from sympy.polys.polytools import degree, lcm_list
  from sympy.sets.sets import Interval, Intersection, FiniteSet, Union, Complement
  from sympy.sets.fancysets import ImageSet
  from sympy.sets.conditionset import ConditionSet
  from sympy.utilities import filldedent
  from sympy.utilities.iterables import iterable
label_desc: Use image node_id 5 for calling a global function with example usage: _periodicity(args, symbol) and returns: lcim, periods, None