Get Closest Value With GROUP BY
After trying multiple times and with the help of the answer here, I was able to get the right query:

SELECT t1.`id`, t1.`BU_ID`, t1.`country_id`, 
       t1.`Name`, t1.`Description`, t1.`Length`, 
       t1.`Width`, t1.`Height`, t3.min_lwh
FROM boxes AS t1
JOIN (SELECT MIN(t2.Length * t2.Width * t2.Height) AS min_lwh
      FROM boxes AS t2 WHERE (t2.Length * t2.Width * t2.Height) &gt;= 3775
   ) AS t3
ON (t1.Length * t1.Width * t1.Height) = t3.min_lwh;