From the positive integers 1-100, create a set of integers, such that each pair of integers has a different lowest common multiple. For example, {2, 3, 4, 5} would work because all six LCMs are unique, but {2, 5, 6, 9} would not because LCM(2,9) = LCM(6,9) = 18. Try to find the largest such set. You could just use {all primes}, but can you find larger?
Extension: Find a set of 10 integers, such that each pair of integers has a different LCM, and the largest element of the set is as small as possible.
Source: Original.