Lcd Fractions 1Ca9C7

1. **State the problem:** We need to find the least common denominator (LCD) of the fractions $\frac{1}{10}$ and $\frac{8}{15}$. 2. **Recall the formula:** The LCD of two fractions is the least common multiple (LCM) of their denominators. Here, the denominators are $10$ and $15$. 3. **Find the prime factorizations:** - $10 = 2 \times 5$ - $15 = 3 \times 5$ 4. **Find the LCM:** The LCM is found by taking the highest powers of all prime factors appearing in either number. - For $2$: highest power is $2^1$ - For $3$: highest power is $3^1$ - For $5$: highest power is $5^1$ So, $$\text{LCM}(10, 15) = 2 \times 3 \times 5 = 30$$ 5. **Conclusion:** The least common denominator (LCD) of $\frac{1}{10}$ and $\frac{8}{15}$ is $30$.