feat: Modify LCM dataset to generate numbers with LCM less than their product

reasoning_gym/arithmetic/lcm.py

@@ -46,23 +46,32 @@ class LCMDataset:
         self._current_idx += 1
         return item
 
-    def _generate_numbers(self, rng: Random) -> List[int]:
-        """Generate a list of random positive integers"""
+    def _generate_numbers(self, rng: Random) -> Tuple[List[int], int]:
+        """Generate a list of random positive integers and their LCM.
+        Will try up to 3 times to find numbers with LCM < product."""
+        def calculate_product(nums: List[int]) -> int:
+            return reduce(lambda x, y: x * y, nums)
+        
+        for _ in range(3):  # Try up to 3 times to get LCM < product
+            num_count = rng.randint(self.config.min_numbers, self.config.max_numbers)
+            numbers = [rng.randint(self.config.min_value, self.config.max_value) 
+                      for _ in range(num_count)]
+            result = reduce(lcm, numbers)
+            if result < calculate_product(numbers):
+                return numbers, result
+        
+        # If we failed to find LCM < product after 3 tries, generate one final set
         num_count = rng.randint(self.config.min_numbers, self.config.max_numbers)
-        return [rng.randint(self.config.min_value, self.config.max_value) 
-                for _ in range(num_count)]
-
-    def _calculate_lcm(self, numbers: List[int]) -> int:
-        """Calculate the LCM of a list of numbers"""
-        return reduce(lcm, numbers)
+        numbers = [rng.randint(self.config.min_value, self.config.max_value) 
+                  for _ in range(num_count)]
+        result = reduce(lcm, numbers)
+        return numbers, result
 
     def __getitem__(self, idx: int) -> dict:
         """Generate a single LCM task"""
         rng = Random(self.seed + idx)
         
-        numbers = self._generate_numbers(rng)
-        result = self._calculate_lcm(numbers)
-        
+        numbers, result = self._generate_numbers(rng)
         numbers_str = ", ".join(str(n) for n in numbers)
         
         return {