Which condition is commonly linked to hypothyroidism?

Hashimoto's disease is commonly linked to hypothyroidism because it is an autoimmune disorder wherein the immune system attacks the thyroid gland, leading to inflammation and impaired thyroid function. This typically results in an underactive thyroid (hypothyroidism), where the gland fails to produce sufficient thyroid hormones. The relationship between Hashimoto's disease and hypothyroidism is well established, as many individuals with Hashimoto's eventually develop this condition as the thyroid becomes increasingly damaged by the autoimmune process.

The other options do not have a direct relationship with hypothyroidism. Graves' disease, for example, is an autoimmune disorder that causes hyperthyroidism, resulting in an overproduction of thyroid hormones, which is quite the opposite of hypothyroidism. Cystic fibrosis and diabetes mellitus are unrelated diseases that do not directly impact thyroid function in the same manner, making them less relevant to the question about hypothyroidism.