def get_the_lcm(C_K, embeddings, d, gen_list):
type_2_eps = (6, ) * d
epsilons = {type_2_eps: "type-2"}
running_lcm = 1
for frak_q in gen_list:
nm_q = ZZ(frak_q.absolute_norm())
q, a = nm_q.perfect_power()
q_class_group_order = C_K(frak_q).multiplicative_order()
ordinary_frob_polys = get_ordinary_weil_polys_from_values(q, a)
ABCo_lcm = ABC_integers(embeddings, frak_q, epsilons,
q_class_group_order,
ordinary_frob_polys)[type_2_eps]
running_lcm = lcm([running_lcm, ABCo_lcm, ZZ(nm_q)])
return running_lcm
