/// <summary>
/// Calculates least common multiple of two integer numbers.
/// </summary>
/// <param name="a">First number.</param>
/// <param name="b">Second number.</param>
/// <returns>Least common multiple of <paramref name="a"/> and <paramref name="b"/>.</returns>
/// <exception cref="ArgumentOutOfRangeException"><paramref name="a"/> is zero or negative. -or-
/// <paramref name="b"/> is zero or negative.</exception>
internal static long LeastCommonMultiple(long a, long b)
{
ThrowIfArgument.IsNonpositive(nameof(a), a, "First number is zero or negative.");
ThrowIfArgument.IsNonpositive(nameof(b), b, "Second number is zero or negative.");
long n1, n2;
if (a > b)
{
n1 = a;
n2 = b;
}
else
{
n1 = b;
n2 = a;
}
for (int i = 1; i < n2; i++)
{
if ((n1 * i) % n2 == 0)
{
return(i * n1);
}
}
return(n1 * n2);
}
/// <summary>
/// Divides the specified <see cref="Fraction"/> by positive integer number.
/// </summary>
/// <param name="fraction">The dividend.</param>
/// <param name="number">The divisor.</param>
/// <returns>Quotient of <paramref name="fraction"/> and <paramref name="number"/>.</returns>
/// <exception cref="ArgumentNullException"><paramref name="fraction"/> is null.</exception>
/// <exception cref="ArgumentOutOfRangeException"><paramref name="number"/> is zero or negative.</exception>
public static Fraction operator /(Fraction fraction, long number)
{
ThrowIfArgument.IsNull(nameof(fraction), fraction);
ThrowIfArgument.IsNonpositive(nameof(number), number, "Number is zero or negative.");
return(new Fraction(fraction.Numerator,
fraction.Denominator * number));
}
/// <summary>
/// Initializes a new instance of the <see cref="Fraction"/> with the specified
/// numerator and denominator.
/// </summary>
/// <param name="numerator">The numerator of a fraction.</param>
/// <param name="denominator">The denominator of a fraction.</param>
/// <exception cref="ArgumentOutOfRangeException"><paramref name="numerator"/> is negative. -or-
/// <paramref name="denominator"/> is zero or negative.</exception>
public Fraction(long numerator, long denominator)
{
ThrowIfArgument.IsNegative(nameof(numerator), numerator, "Numerator is negative.");
ThrowIfArgument.IsNonpositive(nameof(denominator), denominator, "Denominator is zero or negative.");
// Simplify a fraction
var greatestCommonDivisor = MathUtilities.GreatestCommonDivisor(numerator, denominator);
numerator /= greatestCommonDivisor;
denominator /= greatestCommonDivisor;
Numerator = numerator;
Denominator = denominator;
}