Pruebe esta consulta:
select *
from
tableA a
inner join
tableB b
on a.common = b.common
inner join
(select * from tableC order by some_column limit 15) c
on b.common = c.common
Pruebe esta consulta:
select *
from
tableA a
inner join
tableB b
on a.common = b.common
inner join
(select * from tableC order by some_column limit 15) c
on b.common = c.common