diff --git a/server/src/internalClusterTest/java/org/opensearch/search/query/SearchQueryIT.java b/server/src/internalClusterTest/java/org/opensearch/search/query/SearchQueryIT.java
index d2bca41760ff6..c8e06f88da0e3 100644
--- a/server/src/internalClusterTest/java/org/opensearch/search/query/SearchQueryIT.java
+++ b/server/src/internalClusterTest/java/org/opensearch/search/query/SearchQueryIT.java
@@ -394,7 +394,19 @@ public void testCommonTermsQuery() throws Exception {
         assertSecondHit(searchResponse, hasId("2"));
         assertThirdHit(searchResponse, hasId("3"));
 
-        searchResponse = client().prepareSearch().setQuery(commonTermsQuery("field1", "the huge fox").lowFreqMinimumShouldMatch("2")).get();
+        // cutoff frequency of 1 makes all terms high frequency so the query gets rewritten as a
+        // conjunction of all terms (the lowFreqMinimumShouldMatch parameter is effectively ignored)
+        searchResponse = client().prepareSearch()
+            .setQuery(commonTermsQuery("field1", "the huge fox").cutoffFrequency(1).lowFreqMinimumShouldMatch("2"))
+            .get();
+        assertHitCount(searchResponse, 1L);
+        assertFirstHit(searchResponse, hasId("2"));
+
+        // cutoff frequency of 100 makes all terms low frequency, so lowFreqMinimumShouldMatch=3
+        // means all terms must match
+        searchResponse = client().prepareSearch()
+            .setQuery(commonTermsQuery("field1", "the huge fox").cutoffFrequency(100).lowFreqMinimumShouldMatch("3"))
+            .get();
         assertHitCount(searchResponse, 1L);
         assertFirstHit(searchResponse, hasId("2"));