You can Obtain This type of problems by simplifying the given equation
Let us Consider above equation as R=(R1+R2)* so this equation we can convert as some basics forms
R=(R1*+R2*)*
R=(R1+R2*)*
R=(R1*.R2*)*
let us take L=(1+1111)*as L=(R1+R2)*
from R1 we can get min length of strings are=0,1,2,3,4,5,6,...etc(all are multiple of 1)
from R2 we can get min length of string are =0,4,8,12,16 (all are multiple of 4)
by observing above min.length string from R1 you can Implement R2 (because R2 subset of R1 we can consider or GCD(R1,R2) is 1)
so With only R1 you can implement whole Language generated by (R1+R2)*
so the Languages is L=1*
so to construct L we need 1 min no of DFA's