Least Common Multiple

Easy
15
77.4% Acceptance

Your task is to implement a method calculateLCM in the Main class that calculates the Least Common Multiple (LCM) of an array of integers.

What is LCM?

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of these integers without leaving a remainder. For example, the LCM of 4 and 5 is 20, as 20 is the smallest number that both 4 and 5 can divide into without a remainder.

Task

Implement the calculateLCM method that takes an array of integers as input and returns their LCM. This method should be public, static, and reside within the Main class.

Challenges

You will face three challenges:

  1. Small, Consecutive Integers: Calculate the LCM of an array [1, 2, 3, 4].
  2. Multiples of 5 and 3: Find the LCM of [15, 20, 25].
  3. Common Factor Numbers: Determine the LCM for [12, 18].

Edge Cases to Consider

  • Empty Array: Your method should handle an empty array gracefully. You may choose to return a default value or throw an exception in this case.
  • Single Element: If the array contains only one element, the LCM is the number itself.
  • Negative Numbers: Consider how your method should behave with negative numbers. Typically, LCM is considered for positive integers, but handling negatives gracefully (e.g., by taking absolute values) might be necessary.
  • Large Numbers: Ensure your method can handle large integers without running into performance issues or integer overflows.

Challenges Information

Challenge 1: Handling Small, Consecutive Integers

  • Task: Implement the calculateLCM method to find the LCM of a small set of consecutive integers. This method should be in a class named Main and should be public and static.
  • Input: An array containing [1, 2, 3, 4].
  • Expected Behavior: Your method should return 12, as the LCM of 1, 2, 3, and 4 is 12.
  • Hint: Consider how you can find the LCM of multiple numbers and handle an array as input.

Challenge 2: Working with Multiples of 5 and 3

  • Task: Modify the calculateLCM method in the Main class to correctly calculate the LCM of numbers, particularly focusing on multiples of 5 and 3.
  • Input: An array containing [15, 20, 25].
  • Expected Behavior: The method should return 300, as the LCM of 15, 20, and 25 is 300.
  • Hint: This set of numbers requires careful consideration of common multiples and factors.

Challenge 3: Dealing with Evenly Spaced Numbers

  • Task: Ensure the calculateLCM method in the Main class accurately calculates the LCM of a pair of numbers with a common factor.
  • Input: An array containing [12, 18].
  • Expected Behavior: The method should return 36, as the LCM of 12 and 18 is 36.
  • Hint: Look into how factors of these numbers can help determine their LCM efficiently.