1. **State the problem:** We need to find the Least Common Multiple (LCM) of two numbers given that their product is 2112 and their Highest Common Factor (HCF) is 4. 2. **Recall the formula:** For any two numbers $a$ and $b$, the product of the numbers equals the product of their LCM and HCF: $$a \times b = \text{LCM}(a,b) \times \text{HCF}(a,b)$$ 3. **Apply the formula:** Given $a \times b = 2112$ and $\text{HCF}(a,b) = 4$, substitute these values: $$2112 = \text{LCM}(a,b) \times 4$$ 4. **Solve for LCM:** Divide both sides by 4: $$\frac{2112}{\cancel{4}} = \text{LCM}(a,b) \times \cancel{4}$$ $$\text{LCM}(a,b) = \frac{2112}{4}$$ 5. **Calculate the value:** $$\text{LCM}(a,b) = 528$$ **Final answer:** The LCM of the two numbers is $528$.