How to concatenate list of integers into a single number

FromDigits @ StringJoin @ IntegerString @ L

13580

FromDigits @ StringJoin @ IntegerString @ {13, 5, 38, 13}

1353813

Or FromDigits:

FromDigits[{13, 5, 8, 0}]

13580

You can convert the list numbers to strings, then join and finally convert back to number:

L = {13, 5, 8, 0};

ToExpression[StringJoin[ToString /@ L]]
(* 13580 *)