diff --git a/plans/objchange/lcs.go b/plans/objchange/lcs.go
new file mode 100644
index 0000000000..cbfefddddb
--- /dev/null
+++ b/plans/objchange/lcs.go
@@ -0,0 +1,104 @@
+package objchange
+
+import (
+	"github.com/zclconf/go-cty/cty"
+)
+
+// LongestCommonSubsequence finds a sequence of values that are common to both
+// x and y, with the same relative ordering as in both collections. This result
+// is useful as a first step towards computing a diff showing added/removed
+// elements in a sequence.
+//
+// The approached used here is a "naive" one, assuming that both xs and ys will
+// generally be small in most reasonable Terraform configurations. For larger
+// lists the time/space usage may be sub-optimal.
+//
+// A pair of lists may have multiple longest common subsequences. In that
+// case, the one selected by this function is undefined.
+func LongestCommonSubsequence(xs, ys []cty.Value) []cty.Value {
+	if len(xs) == 0 || len(ys) == 0 {
+		return make([]cty.Value, 0)
+	}
+
+	c := make([]int, len(xs)*len(ys))
+	eqs := make([]bool, len(xs)*len(ys))
+	w := len(xs)
+
+	for y := 0; y < len(ys); y++ {
+		for x := 0; x < len(xs); x++ {
+			eqV := xs[x].Equals(ys[y])
+			eq := false
+			if eqV.IsKnown() && eqV.True() {
+				eq = true
+				eqs[(w*y)+x] = true // equality tests can be expensive, so cache it
+			}
+			if eq {
+				// Sequence gets one longer than for the cell at top left,
+				// since we'd append a new item to the sequence here.
+				if x == 0 || y == 0 {
+					c[(w*y)+x] = 1
+				} else {
+					c[(w*y)+x] = c[(w*(y-1))+(x-1)] + 1
+				}
+			} else {
+				// We follow the longest of the sequence above and the sequence
+				// to the left of us in the matrix.
+				l := 0
+				u := 0
+				if x > 0 {
+					l = c[(w*y)+(x-1)]
+				}
+				if y > 0 {
+					u = c[(w*(y-1))+x]
+				}
+				if l > u {
+					c[(w*y)+x] = l
+				} else {
+					c[(w*y)+x] = u
+				}
+			}
+		}
+	}
+
+	// The bottom right cell tells us how long our longest sequence will be
+	seq := make([]cty.Value, c[len(c)-1])
+
+	// Now we will walk back from the bottom right cell, finding again all
+	// of the equal pairs to construct our sequence.
+	x := len(xs) - 1
+	y := len(ys) - 1
+	i := len(seq) - 1
+
+	for x > -1 && y > -1 {
+		if eqs[(w*y)+x] {
+			// Add the value to our result list and then walk diagonally
+			// up and to the left.
+			seq[i] = xs[x]
+			x--
+			y--
+			i--
+		} else {
+			// Take the path with the greatest sequence length in the matrix.
+			l := 0
+			u := 0
+			if x > 0 {
+				l = c[(w*y)+(x-1)]
+			}
+			if y > 0 {
+				u = c[(w*(y-1))+x]
+			}
+			if l > u {
+				x--
+			} else {
+				y--
+			}
+		}
+	}
+
+	if i > -1 {
+		// should never happen if the matrix was constructed properly
+		panic("not enough elements in sequence")
+	}
+
+	return seq
+}
diff --git a/plans/objchange/lcs_test.go b/plans/objchange/lcs_test.go
new file mode 100644
index 0000000000..9b57f4e9dc
--- /dev/null
+++ b/plans/objchange/lcs_test.go
@@ -0,0 +1,100 @@
+package objchange
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/zclconf/go-cty/cty"
+)
+
+func TestLongestCommonSubsequence(t *testing.T) {
+	tests := []struct {
+		xs   []cty.Value
+		ys   []cty.Value
+		want []cty.Value
+	}{
+		{
+			[]cty.Value{},
+			[]cty.Value{},
+			[]cty.Value{},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(3), cty.NumberIntVal(4)},
+			[]cty.Value{},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(2)},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(1)},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(2), cty.NumberIntVal(1)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2)},
+			[]cty.Value{cty.NumberIntVal(1)}, // arbitrarily selected 1; 2 would also be valid
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2), cty.NumberIntVal(3), cty.NumberIntVal(4)},
+			[]cty.Value{cty.NumberIntVal(2), cty.NumberIntVal(4), cty.NumberIntVal(5)},
+			[]cty.Value{cty.NumberIntVal(2), cty.NumberIntVal(4)},
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2), cty.NumberIntVal(3), cty.NumberIntVal(4)},
+			[]cty.Value{cty.NumberIntVal(4), cty.NumberIntVal(2), cty.NumberIntVal(5)},
+			[]cty.Value{cty.NumberIntVal(4)}, // 2 would also be valid
+		},
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(2), cty.NumberIntVal(3), cty.NumberIntVal(5)},
+			[]cty.Value{cty.NumberIntVal(2), cty.NumberIntVal(4), cty.NumberIntVal(5)},
+			[]cty.Value{cty.NumberIntVal(2), cty.NumberIntVal(5)},
+		},
+
+		// unknowns never compare as equal
+		{
+			[]cty.Value{cty.NumberIntVal(1), cty.UnknownVal(cty.Number), cty.NumberIntVal(3)},
+			[]cty.Value{cty.NumberIntVal(1), cty.UnknownVal(cty.Number), cty.NumberIntVal(3)},
+			[]cty.Value{cty.NumberIntVal(1), cty.NumberIntVal(3)},
+		},
+		{
+			[]cty.Value{cty.UnknownVal(cty.Number)},
+			[]cty.Value{cty.UnknownVal(cty.Number)},
+			[]cty.Value{},
+		},
+	}
+
+	for _, test := range tests {
+		t.Run(fmt.Sprintf("%#v,%#v", test.xs, test.ys), func(t *testing.T) {
+			got := LongestCommonSubsequence(test.xs, test.ys)
+
+			wrong := func() {
+				t.Fatalf(
+					"wrong result\nX:    %#v\nY:    %#v\ngot:  %#v\nwant: %#v",
+					test.xs, test.ys, got, test.want,
+				)
+			}
+
+			if len(got) != len(test.want) {
+				wrong()
+			}
+
+			for i := range got {
+				if got[i] == cty.NilVal {
+					wrong()
+				}
+				if !got[i].RawEquals(test.want[i]) {
+					wrong()
+				}
+			}
+		})
+	}
+}