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## Compile time GCD and LCM determination

Header: <boost/math/common_factor_ct.hpp>

    typedef unspecified static_gcd_type;

    template < static_gcd_type Value1, static_gcd_type Value2 >
    struct boost::math::static_gcd : public mpl::integral_c<static_gcd_type, implementation_defined>
    {
    };

    template < static_gcd_type Value1, static_gcd_type Value2 >
    struct boost::math::static_lcm : public mpl::integral_c<static_gcd_type, implementation_defined>
    {
    };

The type `static_gcd_type` is the widest unsigned-integer-type that is supported for use in integral-constant-expressions by the compiler. Usually this the same type as `boost::uintmax_t`, but may fall back to being `unsigned long` for some older compilers.

The boost::math::static_gcd and boost::math::static_lcm class templates take two value-based template parameters of the static_gcd_type type and inherit from the type `boost::mpl::integral_c`. Inherited from the base class, they have a member value that is the greatest common factor or least common multiple, respectively, of the template arguments. A compile-time error will occur if the least common multiple is beyond the range of `static_gcd_type`.

#### Example

    #include <boost/math/common_factor.hpp>
    #include <algorithm>
    #include <iterator>
    #include <iostream>

    int main()
    {
       using std::cout;
       using std::endl;

       cout << "The GCD and LCM of 6 and 15 are "
       << boost::math::gcd(6, 15) << " and "
       << boost::math::lcm(6, 15) << ", respectively."
       << endl;

       cout << "The GCD and LCM of 8 and 9 are "
       << boost::math::static_gcd<8, 9>::value
       << " and "
       << boost::math::static_lcm<8, 9>::value
       << ", respectively." << endl;

       int  a[] = { 4, 5, 6 }, b[] = { 7, 8, 9 }, c[3];
       std::transform( a, a + 3, b, c, boost::math::gcd_evaluator<int>() );
       std::copy( c, c + 3, std::ostream_iterator<int>(cout, " ") );
    }