求最小公倍数和最大公约数
下面的方法是用递归解决的。如求几个整数的最小公倍数的时候，先求前两个的最小公倍数，然后求这个数与第三个数的最小公倍数，依次，即可求出。



Java代码
public class LeastCommonMultiple
{
public static void main(String[] args)
{
int[] arr = {6, 9, 3, 12};
int result = -1;

LeastCommonMultiple lcm = new LeastCommonMultiple();

result = lcm.getMinCommonMultiple(arr);
System.out.println(result);

result = lcm.getMaxDivisor(arr);
System.out.println(result);
}

public int getMinCommonMultiple(int[] arr)
{
int result = arr[0];

for(int i=1; i<arr.length; i++)
{
result = getMinCommonMultiple(result, arr[i]);
}

return result;
}

public int getMaxDivisor(int[] arr)
{
int result = arr[0];

for(int i=1; i<arr.length; i++)
{
result = getMaxDivisor(result, arr[i]);
}

return result;
}

public int getMinCommonMultiple(int a, int b)
{
int result = -1;
int temp = -1;

temp = getMaxDivisor(a, b);

result = a * b;
result = result / temp;

return result;
}

public int getMaxDivisor(int a, int b)
{
int temp = -1;

if(a < b)
{
temp = a;
a = b;
b = temp;
}

while(b != 0)
{
a = a % b;
temp = a;
a = b;
b = temp;
}

return a;
}
}

public class LeastCommonMultiple
{
public static void main(String[] args)
{
int[] arr = {6, 9, 3, 12};
int result = -1;

LeastCommonMultiple lcm = new LeastCommonMultiple();

result = lcm.getMinCommonMultiple(arr);
System.out.println(result);

result = lcm.getMaxDivisor(arr);
System.out.println(result);
}

public int getMinCommonMultiple(int[] arr)
{
int result = arr[0];

for(int i=1; i<arr.length; i++)
{
result = getMinCommonMultiple(result, arr[i]);
}

return result;
}

public int getMaxDivisor(int[] arr)
{
int result = arr[0];

for(int i=1; i<arr.length; i++)
{
result = getMaxDivisor(result, arr[i]);
}

return result;
}

public int getMinCommonMultiple(int a, int b)
{
int result = -1;
int temp = -1;

temp = getMaxDivisor(a, b);

result = a * b;
result = result / temp;

return result;
}

public int getMaxDivisor(int a, int b)
{
int temp = -1;

if(a < b)
{
temp = a;
a = b;
b = temp;
}

while(b != 0)
{
a = a % b;
temp = a;
a = b;
b = temp;
}

return a;
}
}
输出为：



Java代码
36
3