Question

The L.C.M of 6,12 and n is 660 . Find all the possible values of n.

Answer 1

Possible values of "n":

`n= 55\\\\n= 110\\\\n= 220\\\\n=165\\\\n= 330\\\\n= 660`

Explanation:

The first step is to descompose the numbers 6,12 and 660 into their prime factors:

`6=2*3\\\\12=2*2*3=2^2*3\\\\660=2*2*3 *5 * 11=2^2*3*5*11`

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:

`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`