Rainbow Building

You are building a rainbow building from \(N\) cubic unit blocks.

First, you put together 3 cubes each to form a group of \(1\times 3\) columns and discard the remaining cubes.

Then, you put together 5 columns each to form a group of \(3\times 5\) cubic bases and discard the remaining columns, as before.

Finally, you stack 7 bases over one another to build a desired \(3\times 5\times 7\) cuboid structure, as shown above, and discard all the other bases, 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 \(N\)?

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