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Multiple Lowest Common Multiples

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.

Solution

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