Is Number of Subarrays With LCM Equal to K easy or hard?

The problem is rated Medium because the brute force idea is straightforward but the key optimization requires recognizing number theory constraints on LCM values. Understanding how LCM grows and when to prune the search is the main challenge.

Number of Subarrays With LCM Equal to K Python/Java solution

In Python or Java, iterate through each starting index and maintain a running LCM using the formula lcm(a,b) = (a*b)/gcd(a,b). Stop expanding the subarray if the LCM becomes larger than k or does not divide k. This optimized strategy runs in about O(n log k) time.

How to solve Number of Subarrays With LCM Equal to K in O(n)?

A strict O(n) worst-case solution is uncommon because each step involves GCD calculations while extending subarrays. The practical optimal approach is near-linear, around O(n log k), using incremental LCM updates and pruning whenever the current LCM exceeds k or stops dividing k.

What is the best approach for Number of Subarrays With LCM Equal to K?

The most effective solution expands each subarray while maintaining a running LCM and stops early when the LCM exceeds k or no longer divides k. This pruning drastically reduces unnecessary checks. The approach runs in roughly O(n log k) time because LCM values grow quickly and rely on efficient GCD calculations.

Is Number of Subarrays With LCM Equal to K asked at Google/Amazon/Meta?

Problems involving LCM, GCD, and subarray enumeration frequently appear in interviews at companies like Google, Amazon, and Meta. This problem specifically tests number theory knowledge combined with efficient array iteration and pruning techniques.

What data structure is used in Number of Subarrays With LCM Equal to K?

The solution mainly uses arrays with iterative expansion of subarrays. No complex data structures are required. The core operations rely on number theory functions such as GCD and LCM calculations during traversal.

What is the time complexity of Number of Subarrays With LCM Equal to K?

The brute force approach runs in O(n² log k) because every subarray is explored and each step requires a GCD-based LCM calculation. The optimized solution prunes invalid expansions early, reducing the average complexity to about O(n log k) with constant auxiliary space.

Description Hints 3 Solution Video 10:23

2470. Number of Subarrays With LCM Equal to K

Medium47.6% acceptance3 companies

Given an integer array nums and an integer k, return the number of subarrays of nums where the least common multiple of the subarray's elements is k.

A subarray is a contiguous non-empty sequence of elements within an array.

The least common multiple of an array is the smallest positive integer that is divisible by all the array elements.

Example 1:

Input: nums = [3,6,2,7,1], k = 6
Output: 4
Explanation: The subarrays of nums where 6 is the least common multiple of all the subarray's elements are:
- [3,6,2,7,1]
- [3,6,2,7,1]
- [3,6,2,7,1]
- [3,6,2,7,1]

Example 2:

Input: nums = [3], k = 2
Output: 0
Explanation: There are no subarrays of nums where 2 is the least common multiple of all the subarray's elements.

Constraints:

1 <= nums.length <= 1000
1 <= nums[i], k <= 1000

Asked at 3 companies

Unity

Google Amazon

Topics

Hints open one at a time

Hint 1

The constraints on nums.length are small. It is possible to check every subarray.

Hint 2

To calculate LCM, you can use a built-in function or the formula lcm(a, b) = a * b / gcd(a, b).

Hint 3

As you calculate the LCM of more numbers, it can only become greater. Once it becomes greater than k, you know that any larger subarrays containing all the current elements will not work.

10:23

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