diff --git a/15lanqiao/test5.cpp b/15lanqiao/test5.cpp
index aba1db4..c962995 100644
--- a/15lanqiao/test5.cpp
+++ b/15lanqiao/test5.cpp
@@ -1,10 +1,20 @@
 // lanqiao 19711 宝石组合
 #include<bits/stdc++.h>
 using namespace std;
+/*
+解析:
+唯一分解定理:
+任何一个大于1的自然数N，如果N不是质数，那么N可以唯一分解成有限个质数的乘积
+N1=p1^a1*p2^a2*...*pn^an
+N2=p1^b1*p2^b2*...*pn^bn
+则gcd(N1, N2)=p1^min(a1, b1)*p2^min(a2, b2)*... *pn^min(an, bn)
+则lcm(N1, N2)=p1^max(a1, b1)*p2^max(a2, b2)*...*pn^max(an, bn)
+假设Ha,Hb，Hc相同质因子的幂次分别为x,y,z则题目中的表达式等价于
+x+y+z+max(x,y,z)-max(x,y)-max(x,z)-max(y,z)
+*/
 const int N = 1e5 + 10;
 int a[N];
 vector<int> fac[N], s[N];
-
 int main() {
 	for(int i = 1; i <= 1e5; i++){
 		for(int j = i; j <= 1e5; j += i){