# 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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