Answer: 3 Packages of Cups and 4 Packages of Napkins
So, I believe you had a typo, and meant to say “what is the least number or packages of cups AND napkins that can be bought if each…”
To solve, I counted by the amount in each package until its over 60:
Cups: 24 -> 48 -> 72; Counted 3x, so 3 packs
Napkins: 18 -> 36 -> 54 -> 72; Counted 4x, so 4 packs
*Note: Although you have more than 60, its still the least amount of packs you can buy to give all 60 people at-least 1 of each*