Rainbow Building

You are building a rainbow building from NN cubic unit blocks.

First, you put together 3 cubes each to form a group of 1×31\times 3 columns and discard the remaining cubes.

Then, you put together 5 columns each to form a group of 3×53\times 5 cubic bases and discard the remaining columns, as before.

Finally, you stack 7 bases over one another to build the desired 3×5×73\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 NN is a multiple of 11, what is the least possible value of N?N?


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