COCI Solution Explanation

[Script Coder]

I have been doing the competitions at the COCI, and reading the solutions for them. I have come across one section of code in a solution that I do not understand. Thanks in advance :)

Link to the task: http://www.hsin.hr/coci/contest1_tasks.pdf
(Problem: SNAGA)
Translated solution Code:
(I have a problem understanding lines 37-42)

#include <iostream>
#include <vector>
using namespace std;

int main()
{
	long long A, B, solution = 0;
	cin >> A >> B;

	// LCM = lcm(1, 2, ..., K-1)
	long long LCM = 1;

	int power[100];
	power[2] = 1;
	for (int K = 2; K < 100; K++)
	{
		for (int i = 2; i < K; i++) {
			if (K % i != 0) {
				power[K] = power[i] + 1;
				break;
			}
		}
		long long new_LCM = LCM;
		vector<int> prime_divisors_K;
		for (int p = 2, k = K; k > 1; p++) {
			if (k % p == 0) {
				prime_divisors_K.push_back(p);
				while (k % p == 0) {
					k /= p;
				}
			}
		}
		if ((int)prime_divisors_K.size() == 1) {
			new_LCM *= prime_divisors_K[0];
		}

		solution += (power[K] + 1) * (B/LCM - (A-1)/LCM);

		if (new_LCM > B || new_LCM < 0) break;
		solution -= (power[K] + 1) * (B/new_LCM - (A-1)/new_LCM);

		LCM = new_LCM;
	}
	cout << solution << endl;
}