LCM of expressions
In general to find the LCM of expressions in factored form, you may use this formula: LCM of expression = (common factors with the higher exponent) X (factors not in common). Say for example that I'm trying to find the predicted LCM expression for (x+3)(x-3) [factored form of x^2-9] and the expression (x^2 - 2x -3). So the correct LCM expression is (x+3)(x-3)(x+1). Substitute x=5 (prime), then I'm looking for the LCM of 16 and 12 after substitution and according to the algorithm, the LCM of 16 and 12 should be 96. We know it's not because the real LCM is 48. I mean 96 is still a multiple of both 12 and 16 but it's not the least common multiple. Why? What if you substitute numbers besides the NPVs like x=8 (non-prime)? Will the algorithm correctly identify the least common multiple? How would you explain why the derived LCM expression will NOT always give the LEAST value? Like I say, it will yield a multiple, just not necessarily the least. Thank you.