Solve the Fraction Equation: Finding Denominator in 15a/? = 3/b

$$Let's examine the problem:

$\frac{15a}{?}=\frac{3}{b}$

Remember the fraction reduction operation,

In order for the fraction on the left side to be deemed reducible, all the terms in its denominator should have a common factor. Additionally, we want to reduce the number 15 to obtain the number 3. Furthermore we want to reduce the term $a$ from the fraction's numerator given that in the expression on the right side it doesn't appear as well as simultaneously obtaining the term $b$ in the denominator of the fraction on the right side. Note that this term doesn't appear in the expression in the numerator of the fraction on the left side, therefore we'll choose the expression:

$5ab$

since:

$15=3\cdot5$

Let's verify that with this choice we obtain the expression on the right side:

$\frac{15a}{?}=\frac{3}{b} \\ \downarrow\\ \frac{\not{15}\not{a}}{\textcolor{red}{\not{5}\not{a}b}}\stackrel{?}{= }\frac{3}{b} \\ \downarrow\\ \boxed{\frac{3}{b} \stackrel{!}{= }\frac{3}{b} }$

Therefore this choice is indeed correct.

In other words - the correct answer is answer B.