**Core Concept**
Amenorrhoea due to high levels of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) is a clinical presentation associated with a specific underlying pathophysiological condition. This condition is characterized by the premature activation of the hypothalamic-pituitary-gonadal axis, leading to an early increase in gonadotropin levels.

**Why the Correct Answer is Right**
High levels of LH and FSH are typically seen in cases of premature ovarian failure (POF), also known as premature ovarian insufficiency (POI). In POF, the ovaries stop functioning and producing estrogen, leading to an increase in FSH and LH levels due to the loss of negative feedback from estrogen on the hypothalamus and pituitary gland. This results in amenorrhea, which is the absence of menstruation.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because anovulatory cycles are typically associated with low levels of LH and FSH, not high levels.
**Option B:** This option is incorrect because hyperprolactinemia is associated with galactorrhea and amenorrhea due to the inhibition of GnRH release, but not with high levels of LH and FSH.
**Option C:** This option is incorrect because polycystic ovary syndrome (PCOS) is associated with high levels of androgens and insulin resistance, not high levels of LH and FSH.

**Clinical Pearl / High-Yield Fact**
A key clinical feature of premature ovarian failure (POF) is the presence of hot flashes and night sweats, which are similar to those seen in menopausal women. These symptoms occur due to the decrease in estrogen levels, which affects the hypothalamus and leads to an increase in heat production.

**Correct Answer: C. Polycystic ovary syndrome (PCOS)**