Why is lcm(n) used now instead of $\varphi(n)$ in RSA?
Defining the public and private exponents as inverses modulo φ(N), as originally done for RSA, provides a sufficient (but not necessary) condition for the decryption rule to recover the plaintext from any ciphertext. Since Carmichael’s lambda function is, by definition, the smallest number m such that $a^m \equiv 1 \pmod N$, for any integer a that is relatively prime to N. Thus, it is sufficient to define the public and private exponents as inverses modulo any multiple of λ(N).