This is the greatest-n-per-group problem that comes up frequently on Stack Overflow. Here's how I solve it:
SELECT a.article_id, a.last_modified, c1.last_modified AS last_comment_date
FROM articles AS a
JOIN article_comments AS c1
ON (a.article_id = c2.article_id)
LEFT OUTER JOIN article_comments AS c2
ON (a.article_id = c2.article_id AND c1.last_modified < c2.last_modified)
WHERE c2.article_id IS NULL;
This has a chance of producing more than one row per article unless article_comments.last_modified
is unique. To resolve this, use a tiebreaker. For instance, if there's an auto-incrementing primary key column:
SELECT a.article_id, a.last_modified, c1.last_modified AS last_comment_date
FROM articles AS a
JOIN article_comments AS c1
ON (a.article_id = c2.article_id)
LEFT OUTER JOIN article_comments AS c2
ON (a.article_id = c2.article_id AND (c1.last_modified < c2.last_modified
OR c1.last_modified = c2.last_modified AND c1.comment_id < c2.comment_id))
WHERE c2.article_id IS NULL;