1. **Problem:** Find the Lowest Common Multiple (LCM) of 3 and 10 using the diagram. 2. **Formula and Concept:** The LCM of two numbers is the smallest positive integer that is divisible by both numbers. 3. **Step-by-step:** 1. List multiples of 3: $3, 6, 9, 12, 15, 18, 21, 24, 27, 30, \ldots$ 2. List multiples of 10: $10, 20, 30, 40, 50, \ldots$ 3. Identify the smallest common multiple: Both lists share $30$ as the first common multiple. 4. **Explanation:** The LCM is where the groups of 3 and 10 align, which is at 30. 5. **Final answer:** $$\boxed{30}$$