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But there’s a well-known problem: smallest number divisible by 7, 11, 13 is 1001.
But perhaps the problem meant: smallest three-digit number divisible by **7**, **by 11**, and **by 13**—same thing.
Unless the school year is 1001 days? Unlikely.
But to resolve: perhaps the intended number is **the** least such, which is 1001, but since it’s four-digit, the problem may have a typo.
But in olympiad style, perhaps we find the smallest three-digit number divisible by **at least one**, but that’s not “and”.
Alternatively, suppose the problem meant: divisible by **the sum** or **difference**—but not stated.
Given the constraints, and the only multiple of 7,11,13 in a range is 1001, and it’s four digits, **no** such three-digit number exists.
But this cannot be the intended answer.
Wait—perhaps “divisible by 7, 11, and 13” means the number is divisible by **each**, but we can scale down? No.
Unless the number is not required to be three-digit, but the context says “three-digit integer $ z $”.
