feat: Add LCM dataset generator for arithmetic reasoning tasks

reasoning_gym/arithmetic/lcm.py

@@ -0,0 +1,95 @@
+"""Least Common Multiple (LCM) task generator"""
+from dataclasses import dataclass
+from random import Random
+from typing import List, Optional, Tuple
+from math import lcm
+from functools import reduce
+
+
+@dataclass
+class LCMConfig:
+    """Configuration for LCM task generation"""
+    min_numbers: int = 2       # Minimum numbers to find LCM of
+    max_numbers: int = 2       # Maximum numbers to find LCM of
+    min_value: int = 1        # Minimum value for each number
+    max_value: int = 100      # Maximum value for each number (kept smaller than GCD default since LCM grows fast)
+    seed: Optional[int] = None
+    size: int = 500          # Virtual dataset size
+
+    def validate(self):
+        """Validate configuration parameters"""
+        assert self.min_numbers >= 2, "min_numbers must be at least 2"
+        assert self.max_numbers >= self.min_numbers, "max_numbers must be >= min_numbers"
+        assert self.min_value >= 1, "min_value must be positive"
+        assert self.max_value > self.min_value, "max_value must be > min_value"
+
+
+class LCMDataset:
+    """Generates Least Common Multiple (LCM) tasks"""
+
+    def __init__(self, config: LCMConfig):
+        self.config = config
+        self.config.validate()
+        self.seed = config.seed if config.seed is not None else Random().randint(0, 2**32)
+
+    def __len__(self) -> int:
+        return self.config.size
+
+    def __iter__(self):
+        self._current_idx = 0
+        return self
+
+    def __next__(self):
+        if self._current_idx >= self.config.size:
+            raise StopIteration
+        item = self[self._current_idx]
+        self._current_idx += 1
+        return item
+
+    def _generate_numbers(self, rng: Random) -> List[int]:
+        """Generate a list of random positive integers"""
+        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)
+
+    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_str = ", ".join(str(n) for n in numbers)
+        
+        return {
+            "question": f"Find the Least Common Multiple (LCM) of these numbers: {numbers_str}",
+            "answer": str(result),
+            "metadata": {
+                "numbers": numbers,
+                "result": result
+            }
+        }
+
+
+def lcm_dataset(
+    min_numbers: int = 2,
+    max_numbers: int = 2,
+    min_value: int = 1,
+    max_value: int = 100,
+    seed: Optional[int] = None,
+    size: int = 500,
+) -> LCMDataset:
+    """Create a LCMDataset with the given configuration."""
+    config = LCMConfig(
+        min_numbers=min_numbers,
+        max_numbers=max_numbers,
+        min_value=min_value,
+        max_value=max_value,
+        seed=seed,
+        size=size,
+    )
+    return LCMDataset(config)