       Re: Common Multiple Value Question

• To: mathgroup at smc.vnet.net
• Subject: [mg88249] Re: Common Multiple Value Question
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Tue, 29 Apr 2008 06:51:34 -0400 (EDT)

```On 4/28/08 at 4:40 AM, lrebanks at netvigator.com (Lea Rebanks) wrote:

>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}

From what you've written above it isn't clear to me what result
you want. I don't know what you mean by "common multiple value.
I think what you are asking for is to determine the greatest
common divisor and reduce the values by that divisor.

If so, the built-in function you want is GCD. But for the
particular values you list, the GCD is clearly unity since at
least two of the elements in either list3 or list4 are prime.

The problem you are calling "fractional sequence of values" is
the same problem you refer to as "numerical sequence of values"
since the list of rational values has a common denonimator and
the numerators are the same as your list of integers.