Rajesh has two pieces of electric wire. One \(180\) \(cm\) long and other \(240\) \(cm\) long. He wants to cut them up to produce many pieces of wire that are all of the same length with no wire left over.
1. What is the greatest length that he can make them?
2. Express the number \(180\) as a product of prime.
3. What is the exponent of \(2\) in the prime factorization of \(240\)
4. Find the least number that is divisible by the two number \(180\) and \(240\)