HCF and LCM given sum and difference

Let the numbers be $a$ and $b$. $a + b = 256$ $a - b = 224$ Adding: $2a = 480 \implies a = 240$. Subtracting: $2b = 32 \implies b = 16$. $\text{HCF}(240, 16) = 16$. $\text{LCM}(240, 16) = 240$.