/// <summary>
/// 求两个数的最小公倍数。如果其中有个数为0，则返回0
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static NaturalNumStr LeastCommonMultiple(NaturalNumStr a, NaturalNumStr b)
{
if (a == null || b == null)
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.IllegalValue);
}
//统一计算空间
if (a.Space != b.Space)
{
if (a.Space == OperationSpace.DefaultSpace)
{
a = (NaturalNumStr)a.ChangeOperationSpace(b.Space);
}
else if (b.Space == OperationSpace.DefaultSpace)
{
b = (NaturalNumStr)b.ChangeOperationSpace(a.Space);
}
else
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.NotSameOperationSpace);
}
}
if (a == 0 || b == 0)
{
return(new NaturalNumStr(0, a.Space));
}
return(a * b / GreatestCommonDivisor(a, b));
}
/// <summary>
/// 求两个数的最大公约数。如果其中一个数为0、另一个不为0，则返回不为0的那个数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static NaturalNumStr GreatestCommonDivisor(NaturalNumStr a, NaturalNumStr b)
{
if (a == null || b == null)
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.IllegalValue);
}
var old_a = a;
var old_b = b;
//统一计算空间
if (a.Space != b.Space)
{
if (a.Space == OperationSpace.DefaultSpace)
{
a = (NaturalNumStr)a.ChangeOperationSpace(b.Space);
}
else if (b.Space == OperationSpace.DefaultSpace)
{
b = (NaturalNumStr)b.ChangeOperationSpace(a.Space);
}
else
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.NotSameOperationSpace);
}
}
if (a == 0)
{
if (b == 0)
{
throw new IllegalOperationException();
}
else
{
if (ReferenceEquals(b, old_b))
{
return(new NaturalNumStr(b));
}
else
{
return(b);
}
}
}
else if (b == 0)
{
if (ReferenceEquals(a, old_a))
{
return(new NaturalNumStr(a));
}
else
{
return(a);
}
}
if (b > a)
{
var t = a;
a = b;
b = t;
}
//辗转相除法
while (!b.IsZero)
{
var t = a;
a = b;
b = t % b;
}
if (ReferenceEquals(a, old_a) || ReferenceEquals(a, old_b))
{
return(new NaturalNumStr(a));
}
else
{
return(a);
}
}