Moderate# The Fundamental Theorem of Arithmetic, $\gcd$ and $\text{lcm}$

NUMTH-H2UOF0

Let $a, b \in \mathbb{N} \backslash \{1\}$. It follows from the Fundamental Theorem of Arithmetic that $a = p_{1}^{\alpha_1} \cdots p_{s}^{\alpha_{s}}$ and $b = p_{1}^{\beta_1} \cdots p_{s}^{\beta_{s}}$ for some $s \in \mathbb{N}$, where $p_1, \cdots, p_{s}$ are primes and $\alpha_1, \cdots, \alpha_{s}, \beta_1, \cdots, \beta_{s} \in \mathbb{N} \cup \{0\}$. Which of the following statements are true? Select **ALL** that apply.