LCM and HCF Problem

Let the numbers be $21a$ and $21b$, where $a$ and $b$ are co-primes. We know that Product of numbers $= HCF \times LCM$.

$21a \times 21b = 21 \times 3003 \implies a \times b = 143$

Since 143 factors into $11 \times 13$, the coprime pairs $(a, b)$ can be $(1, 143)$ or $(11, 13)$. Since both numbers must be greater than 21, $a = 11$ and $b = 13$. Numbers are $21 \times 11 = 231$ and $21 \times 13 = 273$.

$\text{Sum} = 231 + 273 = 504$