Author 
Comment/Response 
Bill Simpson

07/09/13 01:15am
A graph can sometimes give some insight, but it is probably best used to guide further questions.
Example
In[1]:= Table[{10^n, N[Log[LCM @@ Range[10^n]]]}, {n, 0, 6}]
Out[1]= {
{1,, 0.},
{10,, 7.83201},
{100, 94.0453},
{1000, 996.681},
{10000, 10013.4},
{100000, 100052.},
{1000000, 999587.}}
I also have a few words that might help with your frustration with Mathematica.
Suppose you know English well, you know how to pronounce a few French words, you start stringing those words together, you assume you are producing perfect French sentences and you are trying to communicate with someone who has zero tolerance for the tiniest flaw in French grammar.
Now if you replace English with mathematics and French with Mathematica then you might begin to have some idea what it is like for you to be dealing with Mathematica, but Mathematica is FAR less forgiving or understanding than the French.
Mathematica has no common sense, Mathematica has no mathematical maturity in the sense that it might try to figure out what you really mean and piece together enough information from your description to be able to give you what you actually need, it doesn't do that.
In some sense everything in Mathematica behaves like cosine, cosine accepts a specific angle and returns a specific result. Cos[] behaves that way. But many parts of are not going to produce anything sensible given logic predicates like n is positive and prime.
If you are going to use some term that Mathematica knows then you will probably have much less frustration if you look up that term in the help system and try to understand exactly what syntax and notation that term requires.
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