How can I pick one child from each family in SQL?

I use SQLite and have a table that contains a list of names, some of them are members of the same family.

'-----------------------------------'
| Id | Last Name | First Name | Age |
------------------------------------|
| 1  | Gordon    | James      |  5  |
| 2  | Gordon    | Mike       | 19  |
| 3  | Gordon    | Sara       |  8  |
| 4  | Gordon    | Cludia     | 25  |
| 5  | Sagget    | Bob        | 22  |
| 6  | Saywer    | Tom        |  9  |
| 7  | Saywer    | Jean       | 20  |
| 8  | Finn      | Hucklberry |  8  |
| 9  | Smith     | John       | 18  |
| 10 | Smith     | Sue        | 39  |
'-----------------------------------'

I need to select all people who are 18 years of age or older, but picking one member only from each family. The query should pick the youngest person who is older than or equal to 18 years old. For the above example, the query should return the following people:

'-----------------------------------'
| Id | Last Name | First Name | Age |
------------------------------------|
| 2  | Gordon    | Mike       | 19  |
| 5  | Sagget    | Bob        | 22  |
| 7  | Saywer    | Jean       | 20  |
| 9  | Smith     | John       | 18  |
'-----------------------------------'

Note that Hucklberry Finn was not part of the output since he does not satisfy the condition of 18 years or older, and he has no siblings or relatives . Therefore, no 'Finn's are picked.

What is the simplest query to achieve the above result?

Here is what I tried:

SELECT
    id,
    last_name,
    first_name,
    age
FROM
    people p
WHERE
    age >= 18
    and age < (
      select min(age) from people where age > 18 and last_name = p.last_name
)

I feel there must be a more correct and efficient way than my attempt.

Filter the table for age >= 18 and agregate:

SELECT id,
       last_name,
       first_name,
       MIN(age) AS age
FROM people
WHERE age >= 18
GROUP BY last_name;

SQLite picks the row with the min age from each group.<br/>

See the demo.<br/>

The typical approach in standard SQL would be to either rank the rows:

SELECT id, last_name, first_name, age
FROM
(
  SELECT
    id,
    last_name,
    first_name,
    age,
    ROW_NUMBER() OVER (PARTITION BY last_name ORDER BY age) AS rn
  FROM people p
  WHERE age >= 18
) ranked
WHERE rn = 1;

or use aggregation

SELECT *
FROM people 
WHERE (last_name, age) IN
(
  SELECT
    last_name,
    MAX(age)
  FROM people p
  WHERE age >= 18
  GROUP BY last_name
);

or use WHERE NOT EXISTS <a younger person >= 18 in the same family>).

WITH eighteen_up AS
(
  SELECT *
  FROM people 
  WHERE age >= 18
)
SELECT *
FROM eighteen_up p
WHERE NOT EXISTS
(
  SELECT null
  FROM eighteen_up younger
  WHERE younger.last_name = p.last_name
  AND younger.age < p.age
);

In SQLite, you can usually get this much simpler, as shown in forpas' answer, because of their special treatment of bare columns that other DBMS don't feature. It has its restrictions with ties though that I am explaining below. For this reason it is not a safe option here.

Update

In the request comments you say that in case there are two (or more) youngest 18+ family members (think of twins), you want to pick only one of them. My first query does this (you'd have to use RANK or DENSE_RANK instead of ROW_NUMBER to get both). My second query does not work as desired then, because it will get both persons. My third query, too, selects both, but can be adjusted to only pick one by replacing AND younger.age < p.age by AND (younger.age < p.age OR (younger.age = p.age AND younger.id < p.id)).

The SQLite-only query shown in forpas' answer will not be guaranteed to work, because it could pick the ID and the first name from different rows. srinivas st's query works as my second one, i.e. will select both rows, too.

Conclusion: The only approach you should never use where ties are possible is the bare-columns approach. Depending on how to deal with ties, pick any of the alternatives.

i think this query helps you to get your desired result

SELECT t1.Id, t1.Last_Name, t1.First_Name, t1.Age
FROM family t1
JOIN (
    SELECT Last_Name, MIN(Age) AS MinAge
    FROM family
    WHERE Age >= 18
    GROUP BY Last_Name
) t2 ON t1.Last_Name = t2.Last_Name AND t1.Age = t2.MinAge
WHERE t1.Age >= 18;