Smallest Common Multiple: Intermediate Javascript Algorithm

Question

Question

Find the smallest common multiple of the provided parameters that can be evenly divided by both, as well as by all sequential numbers in the range between these parameters.

The range will be an array of two numbers that will not necessarily be in numerical order.

For example, if given 1 and 3, find the smallest common multiple of both 1 and 3 that is also evenly divisible by all numbers between 1 and 3. The answer here would be 6.

My Code So Far

function smallestCommons(arr) {
  
  let newArr = [];
  
  let changedArr = arr.sort((a, b)=>{
   
    if(a>b){
      return 1;
    }
   
    if(b>a){
      return -1;
    } else {
      return 0;
    }
  })

  for(let i = changedArr[0]; i < changedArr[1]; i++){
    newArr.push(i);
  }

let answer = changedArr.every((item)=>{
  
})

}


smallestCommons([1,5]);

My Question

I was hoping you would be able to help me understand the question - I have looked into the lowest common multiple, but the 'evenly divisible' throws me off.
I was hoping you could solve the problem, and break down the solution simply.

I am asking a lot, so if you answer it is greatly appreciated!

Note that the lcm operation is commutative and associative. Then for example you have lcm(a, b, c) = lcm (lcm(a, b), c) = lcm (a, lcm (b, c)). If you are able to calculate the lcm for two operands, then you can do it iteratively for any number of operands. — Damien

pank pank · Accepted Answer · 2020-05-19T16:52:05

// since the number is evenly divided by all numbers from min to max
// it is the least common multiple of all numbers in the array [min, min + 1, min + 2, ... max]
const smallestCommonMultiple = (a, b) => {
	const [min, max] = [Math.min(a, b), Math.max(a, b)];
	// create the array from min to max
	const range = [...Array(max - min + 1)].map((_, k) => min + k);
	// greatest common divisor of two numbers
	const gcd = (a, b) => b ? gcd(b, a % b) : Math.abs(a);
	// least common multiple of two numbers
	const lcm = (a, b) => a * b / gcd(a, b);
	// least common multiple of an array of numbers
	const lcma = array => array.reduce(lcm);
	return lcma(range);
}
console.log(smallestCommonMultiple(1, 3));
console.log(smallestCommonMultiple(2, 4));
console.log(smallestCommonMultiple(3, 5));

Smallest Common Multiple: Intermediate Javascript Algorithm

1 Answers