For an edge weighted undirected graph G and an integer k greater than or equal to 2, a k-way cut is a set of edges whose removal leaves G with at least Ic components. We propose a simple approximation algorithm to the minimum Ic-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts. We show that the performance ratio of our algorithm is 2 - 3/k for an odd Ic: and 2 - (3k - 4)/(k(2) - k) for an even Ic. The running time is O(kmn(3) log(n(2)/m)) where n, and m are the numbers of vertices and edges respectively.