using System;
using System.Collections.Generic;
public class Sample {
public static void Main(String[] args) {
var n8 = toFactors(8);
var n12 = toFactors(12);
var uf = unionFactors(n8, n12);//LCM
printFactors(uf);
}
public static void printFactors(Dictionary<long, int> factors){
Console.Write("{ ");
foreach(var factor in factors.Keys){
for(int i=0;i<factors[factor];++i)
Console.Write( factor + " ");
}
Console.WriteLine("}");
}
public static Dictionary<long, int> unionFactors(Dictionary<long, int> af, Dictionary<long, int> bf){
Dictionary<long, int> uf = new Dictionary<long, int>();
foreach(var kv in af){
uf.Add(kv.Key, kv.Value);//copy
}
foreach(var kv in bf){
if(uf.ContainsKey(kv.Key)){
if(kv.Value > uf[kv.Key])//max
uf[kv.Key] = kv.Value;
} else {
uf.Add(kv.Key, kv.Value);
}
}
return uf;
}
public static Dictionary<long, int> toFactors(long num){
var factors = new Dictionary<long, int>();
long n = num, i = 2, sqi = 4;
while(sqi <= n){
while(n % i == 0){
n /= i;
if(factors.ContainsKey(i)){
factors[i] += 1;
} else {
factors.Add(i, 1);
}
}
sqi += 2 * (i++) + 1;
}
if(n != 1 && n != num){
if(factors.ContainsKey(i)){
factors[i] += 1;
} else {
factors.Add(i, 1);
}
}
if(factors.Count == 0)
factors.Add(num, 1);//prime
return factors;
}
}