Step 1: Understand the ask.
We must find which listed hormone is NOT made by the human placenta.
Step 2: Recall placental hormones.
During pregnancy the placenta acts as a temporary endocrine gland and secretes hCG, human placental lactogen, estrogen, and progesterone.
Step 3: Check hCG.
hCG is produced by the developing chorion/placenta soon after implantation and keeps the corpus luteum active. So hCG IS placental.
Step 4: Check estrogen and progesterone.
Both rise sharply in pregnancy and are made by the placenta to maintain the uterus and support the fetus. So both ARE placental.
Step 5: Check LH.
Luteinizing hormone is a gonadotropin from the anterior pituitary, not the placenta. In fact the high placental estrogen and progesterone suppress pituitary LH and FSH through negative feedback.
Step 6: Conclude.
The odd one out is LH, which is option (1).
\[ \boxed{\text{LH}} \]