diff --git a/算法/A类：基本算法/3.9 位运算算法.md b/算法/A类：基本算法/3.9 位运算算法.md
index ab11b926..f26b844c 100644
--- a/算法/A类：基本算法/3.9 位运算算法.md	
+++ b/算法/A类：基本算法/3.9 位运算算法.md	
@@ -17,7 +17,7 @@
 操作 | 性质
 |-----| -----|
 n & (n - 1)  | n中的最后一个1变成0。
-n & (\~n + 1) | lowbit()运算，n中最后一个1保留。
+n & (\~n + 1)<br> n&(n^(n-1)) | lowbit()运算，n中最后一个1保留。
 (\~n) + 1== -n | 计算机中补码表示的-n。位运算取反
 n/2 | 等价于 右移一位 n >> 1
 n*2 | 等价于 左移一位 n << 1
diff --git a/算法/A类：基本算法/4.12 gcd&lcm.md b/算法/A类：基本算法/4.12 gcd&lcm.md
new file mode 100644
index 00000000..021cc3c3
--- /dev/null
+++ b/算法/A类：基本算法/4.12 gcd&lcm.md	
@@ -0,0 +1,112 @@
+## 最大公约数
+
+### 循环法
+
+```
+#include<iostream>
+
+using namespace std;
+
+int gcd1(int x,int y){
+    if(x%y==0){
+        return y;
+    }
+    return gcd1(y,x%y);
+}
+
+int gcd2(int x,int y){
+    int r = x % y;
+    while( r )
+    {
+        x = y;
+        y = r;
+        r = x % y;
+    }
+    return y;
+
+}
+
+int lcm(int x,int y){
+    int k = gcd2(x,y);
+    return x*y/k;
+}
+int main(){
+    int x=60,y=95;
+    cout<<gcd1(x,y);
+    return 0;
+}
+```
+
+### 递归法
+
+
+```
+#include<iostream>
+
+using namespace std;
+
+int gcd1(int x,int y){
+    if(x%y==0){
+        return y;
+    }
+    return gcd1(y,x%y);
+}
+
+int gcd2(int x,int y){
+    int r = x % y;
+    while( r )
+    {
+        x = y;
+        y = r;
+        r = x % y;
+    }
+    return y;
+
+}
+
+int lcm(int x,int y){
+    int k = gcd2(x,y);
+    return x*y/k;
+}
+int main(){
+    int x=60,y=95;
+    cout<<gcd1(x,y);
+    return 0;
+}
+```
+## 最小公倍数
+
+```
+#include<iostream>
+
+using namespace std;
+
+int gcd1(int x,int y){
+    if(x%y==0){
+        return y;
+    }
+    return gcd1(y,x%y);
+}
+
+int gcd2(int x,int y){
+    int r = x % y;
+    while( r )
+    {
+        x = y;
+        y = r;
+        r = x % y;
+    }
+    return y;
+
+}
+
+int lcm(int x,int y){
+    int k = gcd2(x,y);
+    return x*y/k;
+}
+int main(){
+    int x=60,y=95;
+    cout<<gcd1(x,y);
+    return 0;
+}
+```
\ No newline at end of file
diff --git a/算法/A类：基本算法/4.12.cpp b/算法/A类：基本算法/4.12.cpp
new file mode 100644
index 00000000..57f27569
--- /dev/null
+++ b/算法/A类：基本算法/4.12.cpp
@@ -0,0 +1,31 @@
+#include<iostream>
+
+using namespace std;
+
+int gcd1(int x,int y){
+    if(x%y==0){
+        return y;
+    }
+    return gcd1(y,x%y);
+}
+
+int gcd2(int x,int y){
+    int r = x % y;
+    while( r )
+    {
+        x = y;
+        y = r;
+        r = x % y;
+    }
+    return y;
+}
+
+int lcm(int x,int y){
+    int k = gcd2(x,y);
+    return x*y/k;
+}
+int main(){
+    int x=60,y=95;
+    cout<<gcd1(x,y);
+    return 0;
+}
\ No newline at end of file