1. **State the problem:** Find the least common multiple (LCM) of the expressions $6a$ and $2$. 2. **Understand the terms:** The LCM of two expressions is the smallest expression that both original expressions divide into without leaving a remainder. 3. **Factor each term:** - $6a = 2 \times 3 \times a$ - $2 = 2$ 4. **Find the LCM:** - Take the highest powers of all prime factors appearing in either term. - For the factor 2, the highest power is $2^1$. - For the factor 3, it appears only in $6a$ as $3^1$. - For the variable $a$, it appears only in $6a$. 5. **Combine these factors:** $$\text{LCM} = 2 \times 3 \times a = 6a$$ 6. **Final answer:** The LCM of $6a$ and $2$ is $6a$.