I'm trying to prove or disprove the following: Let a_1, ..., a_n be natural numbers such that the least common multiple of EVERY n-1 of them is equal to lcm(a_1, ..., a_n) = m. Is it true that a_i = m for some i? The method I've tried so far is to build systems of equations using the information known to prove it in the positive, but it gets very messy. I've also had no luck finding a counter example. n=2 is easy (it's true), but the method doesn't generalize. Thanks in advance.