Multiples

$\text{lcm}\left(2,3,4\right) = 12$ , and thus $12$ is the smallest such positive integer, and the next one must be $24$ because it's the next one divisible by $12$ .

Hence, the answer is $12+24=\boxed{36}$ .

$As\ by\ observation,\ 12\ is\ the\ smallest\ number\ divisible\ by\ 2,3\ and\ 4\ and\ next\ number\ is\ 24.\ So,\ 24+12=36.\$