Questions: Assume that the expressions given are denominators of fractions. Find the least common denominator. 7 a+21, a^2+3 a A. 7 a^2+3 B. 7 a^2+21 C. 7 a(a+3) D. 7 a+3

Solution Steps

The given expressions are \( 7a + 21 \) and \( a^2 + 3a \). We factor each polynomial:

1. For \( 7a + 21 \): \[ 7a + 21 = 7(a + 3) \]

2. For \( a^2 + 3a \): \[ a^2 + 3a = a(a + 3) \]

From the factorization, we have:

• \( 7(a + 3) \)
• \( a(a + 3) \)

The common factor in both expressions is \( (a + 3) \).

To find the least common denominator (LCD), we take the product of the highest powers of all factors present in the factorizations:

\[ \text{LCD} = 7 \cdot a \cdot (a + 3) \]

Final Answer