Final answer:
Primase is the enzyme that primes both DNA strands during eukaryotic DNA replication, by synthesizing an RNA primer that is required for DNA polymerase to begin DNA synthesis.
Step-by-step explanation:
In eukaryotic (euk) DNA replication, the enzyme that primes both DNA strands is called primase. Primase synthesizes a short RNA primer which serves as a starting point for the DNA polymerases to begin synthesis of the new DNA strands. Once the RNA primers are laid down by primase, DNA polymerase α (alpha) extends these primers with a short stretch of DNA nucleotides. After this initial extension, DNA polymerase α hands off the elongation process to other DNA polymerases, with DNA polymerase ε (epsilon) mainly synthesizing the leading strand and DNA polymerase δ (delta) primarily responsible for the lagging strand synthesis. As the process continues, RNA primers are eventually replaced with DNA, and the gaps between Okazaki fragments on the lagging strand are sealed by DNA ligase.