1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A number theoretical problem

  1. Mar 16, 2015 #1
    Recently I have faced the following problem. I'm given 3 integers a,b and L where LCM(a,b,c)=L and c is another integer. It is worthy of mentioning that the value of c will be smallest i.e if there are many possible values of c then we have to choose the one which is smallest.

    I myself solved this problem partially using the following fact
    LCM(a,b,c)=LCM(LCM(a,b),c)=L.Also I used the following procedure. Firstly,I found out LCM(a,b).Secondly, I divide L by LCM(a,b).

    My procedure works for some cases.For example, if a=3,b=5 and L=30,the value of c will be 2 and my above procedure give correct result for this case. But there are some cases for which my procedure does't work.Here is a example. If a=10,b=15 and L=600 then the value of c will be 200 but my procedure give the value of c, 20. How can I get correct result for the given second case for which my procedure doesn't work?
     
  2. jcsd
  3. Mar 17, 2015 #2

    wabbit

    User Avatar
    Gold Member

    Seems like a good start, you have now reduced the problem to an easier one.
    Let's call that LCM(a,b), l
    Now the problem is,
    Given two integers l and L, find the smallest c such that LCM(l, c)=L
    So how would you go about it ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A number theoretical problem
  1. Numbers problems (Replies: 10)

  2. Number problem (Replies: 5)

Loading...