theorem
  for b be non zero Nat holds a lcm ((n*a+1)*b) = (n*a+1)*(a lcm b)
  proof
    let b be non zero Nat;
    a lcm (a*(n*b) + b) = ((a*n)*b/b+1)*(a lcm b) by LCM2;
    hence thesis by XCMPLX_1:89;
  end;
