Beat me to it!
IntegerDigits will break up the numbers, into sub-lists
IntegerDigits@{12, 35}
{{1, 2}, {3, 5}}
Flatten will break up the sub-lists
Flatten@IntegerDigits@{12, 35}
{1, 2, 3, 5}
FromDigits will make a new integer from the flattened list
FromDigits@Flatten@IntegerDigits@{12, 35}
1235
RightComposition allows the operations to be read from left to right
{12, 35} // RightComposition[IntegerDigits, Flatten, FromDigits]
1235
Another way of saying RightComposition is /*
RightComposition[
IntegerDigits,
Flatten,
FromDigits]
IntegerDigits /* Flatten /* FromDigits
Make a compound operation called joinDigits, or as you like
joinDigits = IntegerDigits /* Flatten /* FromDigits;
Call the new operation on your list
joinDigits[{12, 35}]
1235
joinDigits[{12, 35, 69}]
123569