Smallest Even Multiple

Problem

Given a positive integer n, return _the smallest positive integer that is a multiple ofboth _2 andn.

Examples

Example 1

    
    
    Input: n = 5
    Output: 10
    Explanation: The smallest multiple of both 5 and 2 is 10.
    

Example 2

    
    
    Input: n = 6
    Output: 6
    Explanation: The smallest multiple of both 6 and 2 is 6. Note that a number is a multiple of itself.
    

Constraints

• 1 <= n <= 150

Solution

Method 1 – Simple Math (LCM)

Intuition

The smallest number that is a multiple of both n and 2 is their least common multiple (LCM). For any integer n, LCM(n, 2) is n if n is even, or 2n if n is odd.

Approach

1. If n is even, return n.
2. If n is odd, return 2 * n.

Code

C++

class Solution {
public:
    int smallestEvenMultiple(int n) {
        return n % 2 == 0 ? n : 2 * n;
    }
};

Java

class Solution {
    public int smallestEvenMultiple(int n) {
        return n % 2 == 0 ? n : 2 * n;
    }
}

Python

class Solution:
    def smallestEvenMultiple(self, n: int) -> int:
        return n if n % 2 == 0 else 2 * n

Complexity

• ⏰ Time complexity: O(1) — Constant time arithmetic.
• 🧺 Space complexity: O(1) — No extra space used.