Question 1140911
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            The solution and the answer by @MathLover1 is INCORRECT.


            I can easily give a counter-example.


            Let a= 4, b= 3 and c= 5.


            Then LCM(a,b) = LCM(4,3) = 12;


                         LCM(b,c) = LCM(3,5) = 15  - so,  the premise is satisfied;


                         but LCM(a,c) = LCM(4,5) = 20,  which contradicts to the solution by @Mathlover1.


            I can easily give another counter-example.


            Let a= 12, b= 3 and c= 5.


            Then LCM(a,b) = LCM(12,3) = 12;


                         LCM(b,c) = LCM(3,5) = 15  - so,  the premise is satisfied;


                         but LCM(a,c) = LCM(12,5) = 60,  which contradicts to the solution by @Mathlover1.



            The correct solution is below.



<pre>
1.  The premise  LCM(a,b) = 12  and  LCM(b,c) = 15  implies that

        c is multiple of 5  and  b is not multiple of 4.



2.  Then <U>EITHER</U> "a" is 4  <U>OR</U> "a" is 12,

        and both/each of these two opportunities may have place.



3.  It implies that LCM(a,c) is <U>EITHER</U>  LCM(4,5)  = 20

                                <U>OR</U>      LCM(12,5) = 60,


    and, as my counter-examples above show, each and both these opportunities may have place.



4.  So, the answer to the problem's question is <U>EITHER</U>  20  <U>OR</U>  60.

    Each of these two opportunities may have place.
</pre>

Solved.