What is the optimal time complexity of solving Lowest Common Multiple (LCM)?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Lowest Common Multiple (LCM)?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Lowest Common Multiple (LCM)?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Lowest Common Multiple (LCM)?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Lowest Common Multiple (LCM)

Learn how to solve the 'Lowest Common Multiple (LCM)' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function find_lcm(a, b) that takes two positive integers a and b and returns their Lowest Common Multiple (LCM). The LCM is the smallest positive integer that is divisible by both a and b.

Hint: You can use the relationship LCM(a, b) = (a * b) / GCD(a, b).

Constraints

•1 <= a, b <= 10^6

Examples

Example 1

Input

find_lcm(4, 6)

Output

Explanation

Multiples of 4: 4, 8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The smallest common multiple is 12.

Example 2

Input

find_lcm(3, 5)

Output

Explanation

Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 5: 5, 10, 15, ... The smallest common multiple is 15.

Example 3

Input

find_lcm(12, 18)

Output

Explanation

GCD(12,18) = 6. LCM = (12 * 18) / 6 = 216 / 6 = 36.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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