I'm having trouble with the descriptions... "And associated to the number 55 (5 × 11) would be **all multiples of 55 whose smallest prime factor is 11** (therefore excluding all multiples of 2, 3, 5 and 7)."

What multiple of 55 could have a smallest prime factor of 11--all being multiples of 5? and later:

"Take the number 618 (2 × 3 × 103). Typically, you might associate to it all multiples of 618 whose smallest prime factor is 103."

In the context of these sets, it must have a different meaning, but I'm not seeing it. Can someone explain?