Answer:
"used to"
Step-by-step explanation:
The first sentence reads: "The boys shared many interests when they were young but they don't now". This means that they "used to" have so much in common, but now they're really different. So, in order to make the second sentence match the first in meaning, we need to add the phrase "used to" into the blank.
Reading the new second sentence now: "The boys used to share many interests when they were young but they don't now". It makes sense and runs smoothly, and it means the same as the first.
Hope this helps!