Question

find the lcd for the following rational expressions.
\\(\frac{7}{3a^{3}b^{5}}, \frac{5}{6a^{2}b^{7}}\\)
lcd = \\(\square\\) (simplify your answer.)

Explanation:

Step1: Find LCD of coefficients

The coefficients are 3 and 6. The prime factors of 3 are \(3\), and of 6 are \(2\times3\). So LCD of 3 and 6 is \(2\times3 = 6\).

Step2: Find LCD of \(a\)-terms

For \(a^3\) and \(a^2\), the highest power of \(a\) is \(a^3\).

Step3: Find LCD of \(b\)-terms

For \(b^5\) and \(b^7\), the highest power of \(b\) is \(b^7\).

Step4: Combine all parts

Multiply the LCD of coefficients, \(a\)-terms, and \(b\)-terms: \(6\times a^3\times b^7 = 6a^3b^7\).

Answer:

\(6a^3b^7\)