This article explores JavaScript's missing mathematical functions and provides custom implementations. While JavaScript's Math object offers useful operations, it lacks many commonly used functions found in other languages. We'll cover: Sum, Product, Odd/Even checks, Triangle Numbers, Factorials, Factors, Prime Number checks, Greatest Common Divisor (GCD), and Lowest Common Multiple (LCM).

Key Points:

1. Extending JavaScript's Math Capabilities: We'll create JavaScript functions for essential mathematical operations not included in the standard library. These functions are fundamental in many programming contexts.

2. Efficient Implementations: We'll demonstrate efficient implementations using both iterative (loops) and recursive approaches, showcasing techniques like the reduce() method and the Euclidean algorithm.

3. Practical Applications and Code Optimization: We'll highlight real-world scenarios where these functions are beneficial, emphasizing code clarity and efficiency.

Missing Math Methods:

1. Sum: Calculating the sum of an array's elements. The reduce() method provides a concise solution:

function sum(array) {
  return array.reduce((sum, number) => sum   number, 0);
}

2. Product: Calculating the product of an array's elements. Similar to sum, reduce() is efficient:

function product(array) {
  return array.reduce((total, num) => total * num, 1);
}

3. Odd and Even: Determining if a number is odd or even using the modulo operator (%):

function isEven(number) {
  return number % 2 === 0;
}

function isOdd(number) {
  return number % 2 !== 0;
}

4. Triangle Number: Calculating the nth triangle number using the formula 0.5 n (n 1):

function triangleNumber(n) {
  return 0.5 * n * (n   1);
}

5. Factorial: Calculating the factorial of a number using recursion:

function factorial(n) {
  if (n 

6. Factors: Finding all factors of a number:

function factors(number) {
    let factorsList = [];
    for (let count = 1; count 

7. isPrime: Checking if a number is prime:

function isPrime(number) {
  return factors(number).length === 2;
}

8. GCD (Greatest Common Divisor): Using the Euclidean algorithm for efficiency:

function gcd(a, b) {
  if (b === 0) {
    return a;
  } else {
    return gcd(b, a % b);
  }
}

9. LCM (Lowest Common Multiple): Calculated using the GCD:

function lcm(a, b) {
  return (a * b) / gcd(a, b);
}

These functions enhance JavaScript's mathematical capabilities, providing solutions for common programming tasks. A complete collection of these functions, along with others, is available in a mini-library (link to be provided if available). This demonstrates the power of extending core functionality to meet specific needs.

(FAQs section remains largely the same, but could be slightly rephrased for better flow and conciseness.)