Lowest Common Denominator

LCD.cs

void Main()
{
	var input = new long[,] { {1, 2}, {1, 3}, {1, 4} };
	
	var fractions = 
		from i in Enumerable.Range(0, input.GetUpperBound(0) + 1)
		select Tuple.Create(input[i,0], input[i,1]);
		
	var denoms = fractions.Select(t => t.Item2).ToArray();
	
	var lcd = LCM(denoms);
	
	var normalizedFractions = 
		from f in fractions
		select Tuple.Create(f.Item1 * (lcd/f.Item2), lcd);
				
	var result = String.Join("", normalizedFractions.Select(f => $"({f.Item1},{f.Item2})"));	
	
	result.Dump(); // For LinqPad output	
}

/// Get the factors of specificed long
public IEnumerable<long> FactorsOf(long num)
{
	return 
		from i in Enumerable.Range(1, (int)num)
		where num % i == 0
		select (long)i;
}

/// Greatest Common Devisor of two longs
public long GCD(long num1, long num2)
{
	return FactorsOf(num1).Intersect(FactorsOf(num2)).Max();
}

/// Least Common Multiple of two longs
public long LCM(long num1, long num2)
{
	return (num1 * num2) / GCD(num1, num2);
}

/// Least Common Multiple of a range of numbers
public long LCM(long[] nums)
{
	if (nums.Length == 1) { return nums[0]; }
	return nums.Aggregate(
		LCM(nums[0], nums[1]), 
		(acc, n) => LCM(acc, n));
}