If the answer you want is something like "133.33Ohms", then doing computations with fractions is overkill. Just use the type "double" to do all your operations, and you'll be fine.
If you want to use fractions, the least common denominator is the same thing as the least common multiple. For two numbers, lcm(a,b,)*gcd(a,b)=a*b, so you can compute it as a*(b/gcd(a,b)). The standard method to compute the gcd is Euclid's Algorithm: http://en.wikipedia.org/wiki/Euclid%27s_algorithm
For more than two numbers, notice that lcm(a,b,c) = lcm(lcm(a,b),c)