theorem NATD29:
  for a,b be Integer holds
    |.a*b.| = (a gcd b)*(a lcm b)
  proof
    let a,b be Integer;
    |.a*b.| = |.a.|*|.b.| by COMPLEX1:65
    .= (|.a.|gcd |.b.|)*(|.a.| lcm |.b.|) by NAT_D:29
    .= (a gcd b)*(|.a.| lcm |.b.|) by INT_2:34
    .= (a gcd b)*(a lcm b) by INT_2:33;
    hence thesis;
  end;
