Lcd Fractions 96A20A

1. **State the problem:** We need to find the least common denominator (LCD) of the fractions $\frac{1}{10}$ and $\frac{2}{5}$.\n\n2. **Recall the definition:** The LCD of two fractions is the least common multiple (LCM) of their denominators.\n\n3. **Identify denominators:** The denominators are $10$ and $5$.\n\n4. **Find the prime factorization:**\n- $10 = 2 \times 5$\n- $5 = 5$\n\n5. **Find the LCM:** The LCM is the product of the highest powers of all prime factors appearing in either number.\n- Highest power of $2$ is $2^1$ (from $10$)\n- Highest power of $5$ is $5^1$ (common to both)\n\nSo, $$\text{LCM}(10,5) = 2 \times 5 = 10.$$\n\n6. **Conclusion:** The least common denominator (LCD) of $\frac{1}{10}$ and $\frac{2}{5}$ is $10$.