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Faster Project Euler 005. #1863

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46 changes: 32 additions & 14 deletions Project-Euler/Problem005.js
View file Open in desktop
Original file line number Diff line number Diff line change
@@ -1,20 +1,38 @@
/*
Smallest multiple
import { PrimeFactors } from '../Maths/PrimeFactors.js'

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
*/
/**
* Smallest Multiple
* @link https://projecteuler.net/problem=5
*
* 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
*
* Method: unique factorization
* @link https://en.wikipedia.org/wiki/Least_common_multiple#Using_prime_factorization
* The method used below calculates the Least Common Multiple (LCM) by multiplying the largest powers of the prime factors of the divisors. For example, 8 is the LCM of 2, 4, and 8. The prime factors of these numbers are 2^1, 2^2, and 2^3. We can discard 2^1 and 2^2 since 2^3 is the largest power of 2, leaving us with a result of 2^3 (8).
*/

export const findSmallestMultiple = (maxDivisor) => {
const divisors = Array.from({ length: maxDivisor }, (_, i) => i + 1)
let num = maxDivisor + 1
let result
export function findSmallestMultiple(maxDivisor) {
const maxPowers = {}
for (let divisor = 2; divisor <= maxDivisor; divisor++) {
const factors = PrimeFactors(divisor)

while (!result) {
const isDivisibleByAll = divisors.every((divisor) => num % divisor === 0)
if (isDivisibleByAll) result = num
else num++
// combine/count prime factors
let powers = {}
for (const factor of factors) {
powers[factor] = (powers[factor] ?? 0) + 1
}

// save largest factors
for (const factor in powers) {
if (powers[factor] > (maxPowers[factor] ?? 0)) {
maxPowers[factor] = powers[factor]
}
}
}

return result
// multiply all primes
return Object.entries(maxPowers).reduce(
(product, [prime, power]) => product * Math.pow(prime, power),
1
)
}

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