Numbers given LCM, HCF and ratio

Let the numbers be $x$ and $4x$.

Product of numbers = $\text{LCM} \times \text{HCF}$ $x \times 4x = 84 \times 21 \Rightarrow 4x^2 = 1764 \Rightarrow x^2 = 441 \Rightarrow x = 21$.

Larger number = $4x = 4 \times 21 = 84$.