## Problem Given an integer `n` and a list of integers `factors`, find the smallest integer strictly greater than `n` that is divisible by every element in `factors`. ```python def smallest_divisible(n: int, factors: list[int]) -> int: ... ``` ``` Input: n=10, factors=[3, 4] LCM(3,4) = 12 Smallest multiple of 12 > 10 -> 12 Output: 12 Input: n=12, factors=[3, 4] Must be STRICTLY greater than 12 -> 24 Output: 24 Input: n=0, factors=[5, 7] LCM=35, first multiple > 0 -> 35 Output: 35 ``` ## Follow-ups 1. How do you compute the LCM of a list of numbers? Walk through the GCD-based approach. 2. What is the time complexity of your solution and what are the edge cases (e.g., factors contains 1, or factors contains duplicates)? 3. What if `n` can be up to 10^18? Does your integer arithmetic still work in Python? In Java/C++? 4. Generalize: find the K-th integer greater than N divisible by all factors. How does the formula change?

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Divisible Number: Find the Smallest Integer Greater Than N Divisible by All Given Factors

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Problem Given an integer n and a list of integers factors, find the smallest integer strictly greater than n that is divisible by every element in factors. Follow-ups How do you compute the LCM of a list of numbers? Walk through the GCD-based approach. What is the time complexity of your solution and what are the edge cases (e.g., factors contains 1, or factors contains duplicates)? What if n can be up to 10^18? Does your integer arithmetic still work in Python? In Java/C++? Generalize: find the…

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Divisible Number: Find the Smallest Integer Greater Than N Divisible by All Given Factors

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