Finding the least common multiple (LCM) of two or three numbers using JavaScript

Question

Finding the least common multiple (LCM) of two or three numbers using JavaScript

I have been working on a code snippet to find the Greatest Common Denominator (GCD) of two or three numbers. Here is what I have so far:

Math.GCD = function(numbers) {
  for (var i = 1 ; i < numbers.length ; i++){
    if (numbers[i] || numbers[i] === 0)
      numbers[0] = twogcd(numbers[0], numbers[i]);
  }
  return numbers[0];

  function twogcd(first, second) {
    if (first < 0) first = -first;
    if (second < 0) second = -second;
    if (second > first) {var temp = first; first = second; second = temp;}
    while (true) {
        first %= second;
        if (first == 0) return second;
        second %= first;
        if (second == 0) return first;
    }
   }
};

Math.LCM = function(first,second) {
    return first * (second / this.GCD(first, second)); // STRUGGLING TO EXTEND THIS TO THREE #s
};

// example
console.log(Math.GCD([4, 5, 10]));

Check out the live example on JSFiddle

Take note of the part in the code related to the Least Common Multiple (LCM)

I am currently attempting to expand this functionality to calculate the LCM of either two or three user-inputted values. Unfortunately, I'm having trouble getting it right. As an amateur in JavaScript, any assistance would be greatly appreciated. Remember that if a value is left empty, it should not be included in the computation similarly to how it's done with the GCD.

javascript math

Answer 1

Answer №1

If you're looking to find the greatest common divisor or least common multiple of a list of integers, here are some useful functions:

function findGCD(a, b) {
  // Find the greatest common divisor of two integers
  if(!b) return b===0 ? a : NaN;
  return findGCD(b, a%b);
}
function findGCDFromArray(array) {
  // Find the greatest common divisor of an array of integers
  var result = 0;
  for(var i=0; i<array.length; ++i)
    result = findGCD(array[i], result);
  return result;
}
function findLCM(a, b) {
  // Find the least common multiple of two integers
  return a*b / findGCD(a, b);
}
function findLCMFromArray(array) {
  // Find the least common multiple of an array of integers
  var result = 1;
  for(var i=0; i<array.length; ++i)
    result = findLCM(array[i], result);
  return result;
}

Answer 2

If you're looking to find the greatest common divisor or least common multiple of a list of integers, here are some useful functions:

function findGCD(a, b) {
  // Find the greatest common divisor of two integers
  if(!b) return b===0 ? a : NaN;
  return findGCD(b, a%b);
}
function findGCDFromArray(array) {
  // Find the greatest common divisor of an array of integers
  var result = 0;
  for(var i=0; i<array.length; ++i)
    result = findGCD(array[i], result);
  return result;
}
function findLCM(a, b) {
  // Find the least common multiple of two integers
  return a*b / findGCD(a, b);
}
function findLCMFromArray(array) {
  // Find the least common multiple of an array of integers
  var result = 1;
  for(var i=0; i<array.length; ++i)
    result = findLCM(array[i], result);
  return result;
}

Answer 3

Answer №2

If you tweak the structure slightly for GCD and LCM, both methods can be streamlined to have just two arguments.

To calculate the result for more than two arguments, utilize Array.prototype.reduce(). This method selects two elements from the array at a time and returns a result, which is then incorporated as a new input until all array elements are processed.

Given that LCM and GCD adhere to the associative property, they can be linked together as needed.

Math.GCD = function twogcd(first, second) {
    if (first < 0) first = -first;
    if (second < 0) second = -second;
    if (second > first) { var temp = first; first = second; second = temp; }
    while (true) {
        first %= second;
        if (first == 0) return second;
        second %= first;
        if (second == 0) return first;
    }
};

Math.LCM = function (first, second) {
    return first * (second / Math.GCD(first, second));
};

document.getElementById('calc').addEventListener('click', function (e) {
    var first = +document.getElementById("first").value,
        second = +document.getElementById("second").value,
        third = +document.getElementById("third").value,
        numbers = [first, second, third],
        resultGCD = numbers.reduce(Math.GCD), // chaining
        resultLCM = numbers.reduce(Math.LCM); // chaining

    document.getElementById('gcd').innerHTML = resultGCD;
    document.getElementById('lcm').innerHTML = resultLCM;
});

GCD: <span id="gcd"></span><br />
LCM: <span id="lcm"></span><br />
<form name="sci-calc" method="POST" id="sci-calc">
    <input type="text" name="stuff[]" class="input-field" id="first" /><br />
    <input type="text" name="stuff[]" class="input-field" id="second" /><br />
    <input type="text" name="stuff[]" class="input-field" id="third" /><br />
    <button type="button" id="calc">CALC</button>
</form>

Answer 4

If you tweak the structure slightly for GCD and LCM, both methods can be streamlined to have just two arguments.

To calculate the result for more than two arguments, utilize Array.prototype.reduce(). This method selects two elements from the array at a time and returns a result, which is then incorporated as a new input until all array elements are processed.

Given that LCM and GCD adhere to the associative property, they can be linked together as needed.

Math.GCD = function twogcd(first, second) {
    if (first < 0) first = -first;
    if (second < 0) second = -second;
    if (second > first) { var temp = first; first = second; second = temp; }
    while (true) {
        first %= second;
        if (first == 0) return second;
        second %= first;
        if (second == 0) return first;
    }
};

Math.LCM = function (first, second) {
    return first * (second / Math.GCD(first, second));
};

document.getElementById('calc').addEventListener('click', function (e) {
    var first = +document.getElementById("first").value,
        second = +document.getElementById("second").value,
        third = +document.getElementById("third").value,
        numbers = [first, second, third],
        resultGCD = numbers.reduce(Math.GCD), // chaining
        resultLCM = numbers.reduce(Math.LCM); // chaining

    document.getElementById('gcd').innerHTML = resultGCD;
    document.getElementById('lcm').innerHTML = resultLCM;
});

GCD: <span id="gcd"></span><br />
LCM: <span id="lcm"></span><br />
<form name="sci-calc" method="POST" id="sci-calc">
    <input type="text" name="stuff[]" class="input-field" id="first" /><br />
    <input type="text" name="stuff[]" class="input-field" id="second" /><br />
    <input type="text" name="stuff[]" class="input-field" id="third" /><br />
    <button type="button" id="calc">CALC</button>
</form>

Answer 5

Answer №3

I haven't quite deciphered the purpose of your code, but I have a function here that can help find the LCM:

LCM = function(numbers) {
  console.log(numbers)  
  if (numbers.length < 2) return
  first = numbers[0]
  second = numbers[1]
  var i = j = 1
  var mult1 = first * i++
  var mult2 = second * j++
  while (mult1 != mult2) {
    if (mult1 < mult2)
        mult1 = first * i++
    else
        mult2 = second * j++
  }
  if (numbers.length > 2) {
    numbers[1] = mult1 //It may modify 'numbers' 
    mult1 = LCM(numbers.splice(1, numbers.length-1))
  }
    return mult1
}

It may not be the most efficient solution, but it demonstrates how you can handle multiple parameters using recursion.

You can see it in action on this fiddle: https://jsfiddle.net/grabantot/fr0gzogL/

Answer 6

I haven't quite deciphered the purpose of your code, but I have a function here that can help find the LCM:

LCM = function(numbers) {
  console.log(numbers)  
  if (numbers.length < 2) return
  first = numbers[0]
  second = numbers[1]
  var i = j = 1
  var mult1 = first * i++
  var mult2 = second * j++
  while (mult1 != mult2) {
    if (mult1 < mult2)
        mult1 = first * i++
    else
        mult2 = second * j++
  }
  if (numbers.length > 2) {
    numbers[1] = mult1 //It may modify 'numbers' 
    mult1 = LCM(numbers.splice(1, numbers.length-1))
  }
    return mult1
}

It may not be the most efficient solution, but it demonstrates how you can handle multiple parameters using recursion.

You can see it in action on this fiddle: https://jsfiddle.net/grabantot/fr0gzogL/

Finding the least common multiple (LCM) of two or three numbers using JavaScript

Answer №1

Answer №2

Answer №3

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