# [C (gcc)], 99 bytes

Adapted from [my JS answer](https://codegolf.stackexchange.com/a/266309/58563). Prints the bounds separated by a space.

<!-- language-all: lang-c -->

 m,M,x,p;f(n){for(M=n*n,m=1,x=p=2;m=(x*=p)>n|x<m?m:x,x<n?1:x<M?M=x:(x=++p)<n;);printf("%d %d",m,M);}

[Try it online!][TIO-lofu8hba]

[C (gcc)]: https://gcc.gnu.org/
[TIO-lofu8hba]: https://tio.run/##fdBLasMwEAbgfU8xBAJSMiF62fVL9Ql8gtJFsHFqqBXhpq0gzdXrKrHrld1ZCAY@fs1MuTuWZd@3WKBDm9bE0Et96kihzcZgqzk6bbVIW03cRlv6ZL5d1uZt4tBlJueJy4q80C4hTm@3lmYmpantGnOuyWpdwbpaoQ@n6bX/PDUVtIfGEAqXB4CaCJqC/TiXr4eOcOabofZ7eOYI6uWOJJtVNyQeEaQYWLDMVIwQjmmczbr7l4wh@GeEIlyEIvBQRAMU/yTGIYLg4d@Ei1BFCiHg0yqzcliFSy@Z4uNxYhUF0@GmulEZS@ZTZRwyj6/9T1m/HY7v/e7rFw "C (gcc) – Try It Online"