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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


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    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 ?
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