Initialize multiple constant class members using one function call C++

The member vars are initialized by the order they are declared in the class declaration, hence you can do the following (mathematically)

#include <iostream>
int gcd(int a, int b){return 2;}; // Greatest Common Divisor of (4, 6) just to test
class Fraction {
public:
    // Lets say we want to initialize to a reduced fraction
    Fraction(int a, int b) : numerator{a/gcd(a,b)}, denominator(b/(a/numerator))
    {    
    }
//private:
    const int numerator, denominator;//make sure that they are in this order
};
//Test
int main(){
    Fraction f{4,6};
    std::cout << f.numerator << " / " << f.denominator;
}

No need for calling another constructors or even making them.

In general, is there a way to do this without wasted function calls or memory?

Yes. This can be done with a delegating constructor, introduced in C++11.

A delegating constructor is a very efficient way to acquire temporary values needed for construction before any member variables are initialized.

int gcd(int a, int b); // Greatest Common Divisor

class Fraction {
public:
    // Call gcd ONCE, and forward the result to another constructor.
    Fraction(int a, int b) : Fraction(a,b,gcd(a,b))
    {
    }
private:
    // This constructor is private, as it is an
    // implementation detail and not part of the public interface.
    Fraction(int a, int b, int g_c_d) : numerator(a/g_c_d), denominator(b/g_c_d)
    {
    }
    const int numerator, denominator;
};