Rainbow BuildingNumber Theory Level 4
You are building a rainbow building from \(N\) cubic unit blocks.
First, you put 3 cubes each to form a group of columns and discard the remaining cubes away.
Then, you put 5 columns together each to form a group of \(3\times 5\) cubic bases and discard the remaining columns away as before.
Finally, you stack 7 bases over one another to build a desired \(3\times 5\times 7\) cuboid structure each, as shown above, and discard all the other bases away as usual.
If there are a total of 52 discarded cubes, and \(N\) is a multiple of 11, what is the least possible value of \(N\)?