The {\em λ-approximate compaction} problem is: given an input array of n values, each either 0 or 1, place each value in an output array so that all the 1's are in the first (1+λ)k array locations, where k is the number of 1's in the input. λ is an accuracy parameter. This problem is of fundamental importance in parallel computation because of its applications to processor allocation and approximate counting. When λ is a constant, the problem is called {\em Linear Approximate Compaction} (LAC). On the CRCW PRAM model, %there is an algorithm that solves approximate compaction in \order{(\log\log n)^3} time for λ=loglogn1, using (loglogn)3n processors. Our main result shows that this is close to the best possible. Specifically, we prove that LAC requires %Ω(loglogn) time using \order{n} processors. We also give a tradeoff between λ and the processing time. For ϵ<1, and λ=nϵ, the time required is Ω(logϵ1)