Because of the nature of this problem, it is probably faster to solve by hand than by writing a program. The least common multiple of a set of numbers depends upon their prime factors. 2520 can be factored down into 2^3 x 3^2 x 5 x 7 as these factors can be used to generate all numbers from 2 to 10. Carrying this on from 11-20, the only new factors are 11, 13, 17, 19, and an additional 2, required for the term 16. When multiplying these together, we find that the answer is 232,792,560. Because this answer is relatively small for a computer, it can be calculated with a by iterating through successively larger numbers and checking each for division by each factor. An example of this method has been attached, but writing a program to find the prime factors and multiplying the proper number is much more efficient and practical for larger numbers.

Also attached is a solver implemented in parallel with nVidia CUDA.