Answer:
Possible values of "n":
[tex]n= 55\\\\n= 110\\\\n= 220\\\\n=165\\\\n= 330\\\\n= 660[/tex]
Step-by-step explanation:
The first step is to descompose the numbers 6,12 and 660 into their prime factors:
[tex]6=2*3\\\\12=2*2*3=2^2*3\\\\660=2*2*3 *5 * 11=2^2*3*5*11[/tex]
Since, by definition, the Least Common Multiple (L.C.M) is the product of the common and non common prime factors with their highest exponents, we can determine that the possible values of "n" are:
[tex]n=11* 5 = 55\\\\n=11*5*2 = 110\\\\n=11*5*2^2= 220\\\\n=11*5*3=165\\\\n=11*5* 3*2= 330\\\\n=11*5*3*2^2 = 660[/tex]
