AND in while loop

why does this code stops at a=1 or b=1? i expect it to stop at a=1 and b=1

a=input('');
b=input('');
x=2;
c=1;
while (a~=1 && b~=1)
    while (mod(a,x)==0) || (mod(b,x)==0)
    c=c*x;
     if (mod(a,x)==0)&&(mod(b,x)==0)
         a=a/x;
         b=b/x;
     elseif mod(a,x)==0
         a=a/x;
     elseif mod(b,x)==0
         b=b/x;
     end
    end
    x=x+1;
end
disp(c)

Answer 1

[Jonas]

it should run if

   ~(a==1 && b==1)

which would equal

a~=1 || b~=1