Here are further words from Wikipedia, to learn against
   later.  [1]https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)

   In the original RSA paper,^[2][2] the [3]Euler totient function φ(n) =
   (p − 1)(q − 1) is used instead of λ(n) for calculating the private
   exponent d. Since φ(n) is always divisible by λ(n) the algorithm works
   as well. That the [4]Euler totient function can be used can also be
   seen as a consequence of [5]Lagrange's theorem applied to
   the [6]multiplicative group of integers modulo pq. Thus
   any d satisfying d⋅e ≡ 1 (mod φ(n)) also satisfies d⋅e ≡ 1 (mod λ(n)).
   However, computing d modulo φ(n) will sometimes yield a result that is
   larger than necessary (i.e. d > λ(n)). Most of the implementations of
   RSA will accept exponents generated using either method (if they use
   the private exponent d at all, rather than using the optimized
   decryption method [7]based on the Chinese remainder theorem described
   below), but some standards such as [8]FIPS 186-4 may require
   that d < λ(n). Any "oversized" private exponents not meeting that
   criterion may always be reduced modulo λ(n) to obtain a smaller
   equivalent exponent.

   Since any common factors of (p − 1) and (q − 1) are present in the
   factorisation of n − 1 = pq − 1 = (p − 1)(q − 1) + (p − 1) + (q −
   1),^[9][17] it is recommended that (p − 1) and (q − 1) have only very
   small common factors, if any besides the necessary
   2.^[10][2]^[11][18]^[12][19]^[13][20]

   Note: The authors of the original RSA paper carry out the key
   generation by choosing d and then computing e as the [14]modular
   multiplicative inverse of d modulo φ(n), whereas most current
   implementations of RSA, such as those following [15]PKCS#1, do the
   reverse (choose e and compute d). Since the chosen key can be small
   whereas the computed key normally is not, the RSA paper's algorithm
   optimizes decryption compared to encryption, while the modern algorithm
   optimizes encryption instead.^[16][2]^[17][21]

References

   1. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)
   2. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-rsa-2
   3. https://en.m.wikipedia.org/wiki/Euler_totient_function
   4. https://en.m.wikipedia.org/wiki/Euler_totient_function
   5. https://en.m.wikipedia.org/wiki/Lagrange's_theorem_(group_theory)
   6. https://en.m.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n
   7. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#Using_the_Chinese_remainder_algorithm
   8. http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=62
   9. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-17
  10. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-rsa-2
  11. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-18
  12. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-19
  13. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-20
  14. https://en.m.wikipedia.org/wiki/Modular_multiplicative_inverse
  15. https://en.m.wikipedia.org/wiki/PKCS1
  16. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-rsa-2
  17. https://en.m.wikipedia.org/wiki/RSA_(cryptosystem)#cite_note-21