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Student Support Forum: 'Solving for when a summation reaches a value.' topicStudent Support Forum > General > Archives > "Solving for when a summation reaches a value."

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Bill Simpson
07/08/13 4:36pm

New users see the word Solve and assume it has far more power than it actually does and will solve anything and everything.

Solve can do very well with linear problems, pretty good with low degree polynomial problems and horribly or not at all with rational functions, trig functions, radicals and especially "special" functions.

"So, I want to know when the LCM of (1,2,3,...,i) reaches 10,000,000,000 digits"

Let's see if we can quickly get an estimate of how large your i needs to be.

In[1]:= ListPlot[Table[Log[LCM @@ Range[i]], {i, 10000}]]

Out[1]= ...NiceAlmostStraightLinePlotSnipped...

After seeing that I might even bet there is a theorem out there in analytic number theory that says something like: The LCM of the first n positive integers is less than or equal to E^n+fudgefactor.

Hummm. Mathworld has some information on this
http://mathworld.wolfram.com/LeastCommonMultiple.html
And it says the prime number theorem implies exactly what I stated in the previous paragraph.

Google for
theorem least common multiple first n integers
turns up lots of promising results.

Now my graph isn't giving you an exact integer answer to your question, but does it give you a place to start?

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Subject (listing for 'Solving for when a summation reaches a value.')
Author Date Posted
Solving for when a summation reaches a value. JD 07/08/13 06:54am
Re: Solving for when a summation reaches a value. Bill Simpson 07/08/13 4:36pm
Re: Re: Solving for when a summation reaches a ... JD 07/08/13 6:42pm
Re: Solving for when a summation reaches a value. Bill Simpson 07/09/13 01:15am
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