**Core Concept**
In breast cancer, prognosis is influenced by histological type, grade, and molecular characteristics. The most aggressive and poor-prognosis type is characterized by its rapid growth rate, high metastatic potential, and lack of hormone receptors.

**Why the Correct Answer is Right**
Invasive lobular carcinoma (ILC) is a type of breast cancer that arises from the lobules of the breast. It is known for its insidious nature, often presenting with a large tumor size and advanced stage at diagnosis. ILC tends to have a higher rate of lymph node metastasis and is more likely to recur after treatment. This is due to its ability to infiltrate and spread through the breast tissue, making it challenging to detect and treat.

**Why Each Wrong Option is Incorrect**
**Option A:** Invasive ductal carcinoma (IDC) is the most common type of breast cancer, but it generally has a better prognosis than ILC. IDC tends to have a more favorable response to treatment and a lower rate of metastasis.

**Option B:** Ductal carcinoma in situ (DCIS) is a non-invasive type of breast cancer that has not spread beyond the ducts. While DCIS can progress to invasive cancer, it is often curable with treatment and generally has a good prognosis.

**Option C:** Inflammatory breast cancer (IBC) is a rare and aggressive type of breast cancer that presents with skin and lymphatic system involvement. While IBC has a poor prognosis, it is not the most common type of breast cancer with poor prognosis.

**Option D:** Medullary carcinoma is a rare type of breast cancer with a relatively favorable prognosis. It is often associated with a better response to treatment and a lower rate of metastasis.

**Clinical Pearl / High-Yield Fact**
Remember that the prognosis of breast cancer is influenced by the histological type, grade, and molecular characteristics. ILC is a poor-prognosis type, and its aggressive nature requires prompt and aggressive treatment.

**Correct Answer: C. Inflammatory breast cancer (IBC) is a rare and aggressive type of breast cancer with a poor prognosis, but the question is likely referring to Inflammatory breast cancer (IBC) is not the most common type of breast cancer with poor prognosis, but rather Invasive Lobular Carcinoma (ILC).