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

$$Let's examine the problem:

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

Now let's think logically, and remember the fraction reduction operation,

For the fraction on the left side to be reducible, we want all the terms in its denominator to have a common factor. Additionally, we want to reduce the number 15 to get the number 3, and also reduce the term $a$ from the fraction's numerator since in the expression on the right side it doesn't appear, and simultaneously get 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 indeed get 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.