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Re: Common Multiple Value Question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg88226] Re: Common Multiple Value Question
*From*: dh <dh at metrohm.ch>
*Date*: Tue, 29 Apr 2008 06:47:25 -0400 (EDT)
*References*: <fv42jv$5va$1@smc.vnet.net>
Hi Lea,
I am not sure if I understand you correctly.
You have two integer sequences, e.g. {a1,a2,a3} and {b1,b2,b3} and you
want a sequence {c1,c2,c3} so that ai and bi divide ci, ci need not be
the LCM and c1:c2:c3 == a1:a2:a3. This can be done by noting that a
possible CM is simply the product. We then only have to deal with
c1:c2:c3 == a1:a2:a3. This can be achieved by mutiplying a1 by b2 b3, a2
by b3 b1 .. This finally gives {a1,a2,a3} b1 b2 b3:
In mathematica this may be written by:
lista={a1,a2,a3}; listb={b1,b2,b3};
listc= lista Times@@ listb
For rational number you must first define what a multiple of a number
is. For every rational r1 besides zero there is another one r2 so that
the product is a given r3. That is every number is a multiple of every
number (besides zero).
hope this the not right answer to the wrong question, Daniel
Lea Rebanks wrote:
> Dear All,
>
> I am trying to solve this Common Multiple Value Question based on 2
> sequences of values...
> This is both a Math question & also a question on how to apply this problem
> to Mathematica.
> However, please note I am trying to find BOTH Common Multiple Value, of each
> element in both lists AND maintaining the same proportion in the first list
> of elements.
>
> I will pose this problem in 2 ways.
> (i) Fractional sequence of values.
> (ii) Numerical sequence of values.
> Actually they are the same question, but I would like to be able to solve
> this in both the fractional & numerical form.
> (... And also solving this without using LCM - Lowest Common Multiple
> function .... as this is part of a bigger calculation & I will be using
> algebra.)
>
> (i) Fractional sequence of values - 1 pair. 3 elements in each.
> list1={2/3,2/3+1,2/3+2}
> list2={3/4,3/4+1,3/4+2}
> {2/3,5/3,8/3}
> {3/4,7/4,11/4}
>
> (ii) Numerical sequence of values - 1 pair. 3 elements in each.
> list3={2,5,8}
> list4={3,7,11}
> {2,5,8}
> {3,7,11}
>
> ( Apologies if this question is so simple... I have been trying to figure
> this out for a number of days ...)
>
> Many thanks for any help or advice. Greatly appreciated.
> Best regards ... Lea Rebanks.
>
>
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