diff --git a/jsonschema/_keywords.py b/jsonschema/_keywords.py
index f30f9541..1fde97f3 100644
--- a/jsonschema/_keywords.py
+++ b/jsonschema/_keywords.py
@@ -168,6 +168,12 @@ def multipleOf(validator, dB, instance, schema):
     if not validator.is_type(instance, "number"):
         return
 
+    # JSON Schema: numbers with zero fractional parts are integers.
+    # Convert integer-valued floats (e.g. 11.0) to int to avoid
+    # floating-point precision loss with large instances.
+    if isinstance(dB, float) and dB.is_integer():
+        dB = int(dB)
+
     if isinstance(dB, float):
         quotient = instance / dB
         try:
diff --git a/jsonschema/tests/test_validators.py b/jsonschema/tests/test_validators.py
index 7d8a4c5c..8021413c 100644
--- a/jsonschema/tests/test_validators.py
+++ b/jsonschema/tests/test_validators.py
@@ -501,6 +501,23 @@ def test_multipleOf(self):
         )
         self.assertEqual(message, "3 is not a multiple of 2")
 
+    def test_multipleOf_integer_valued_float(self):
+        """Integer-valued floats like 11.0 should behave like integers (#1159).
+
+        Large integers beyond 2**53 lose precision in float division,
+        so multipleOf with an integer-valued float must use integer
+        arithmetic to avoid false negatives.
+        """
+        instance = 9007199254740995  # 2**53 + 3, a multiple of 11
+        # With integer divisor this passes
+        validators.Draft202012Validator(
+            {"type": "integer", "multipleOf": 11},
+        ).validate(instance)
+        # With integer-valued float divisor this should also pass
+        validators.Draft202012Validator(
+            {"type": "integer", "multipleOf": 11.0},
+        ).validate(instance)
+
     def test_minItems(self):
         message = self.message_for(instance=[], schema={"minItems": 2})
         self.assertEqual(message, "[] is too short")