Step 1: Understanding the Concept:
This question tests basic knowledge of common names and chemical formulas for alkaline earth metal compounds in s-block chemistry.
Step 2: Key Formula or Approach:
Identify the specific s-block metal whose oxide is universally known as quicklime and whose hydroxide is known as slaked lime.
Step 3: Detailed Explanation:
Let's review the common names of the compounds formed by the given metals:
Sodium (Na): forms $\text{Na}_2\text{O}$ and $\text{NaOH}$ (caustic soda). It does not form $\text{MO}$ type oxides.
Potassium (K): forms $\text{K}_2\text{O}$ and $\text{KOH}$ (caustic potash).
Magnesium (Mg): forms $\text{MgO}$ (magnesia) and $\text{Mg(OH)}_2$ (milk of magnesia).
Calcium (Ca): forms $\text{CaO}$ which is universally known as quicklime, and when reacted with water, it forms $\text{Ca(OH)}_2$, which is known as slaked lime.
Therefore, the metal M representing MO as quicklime and $\text{M(OH)}_2$ as slaked lime is Calcium (Ca).
Step 4: Final Answer:
The metal M is Calcium.