To find the common denominator between two fractions, which of the following operations is NOT necessary?

To find a common denominator between two fractions, it is essential to identify a common value that can uniformly combine the denominators, allowing for the addition or subtraction of the fractions. This process typically involves several operations, but not all are necessary in every calculation.

Identifying the least common multiple (LCM) is a fundamental step because it provides the smallest denominator that both fractions can share. This LCM is crucial for simplifying the fractions and ensuring they are written in a comparable form.

Converting to equivalent fractions is also necessary as this step ensures that each fraction represents the same value but is adjusted to have the newly established common denominator.

Multiplying numerators and denominators accordingly is inherent in this process, as once the least common multiple is established, each fraction is adjusted appropriately. This ensures that the value of the fractions remains unchanged while adopting the common denominator.

Dividing both numerators by the same number, however, is not necessary for finding a common denominator. Division does not contribute to the simplification or adjustment toward a common denominator. Instead, the focus remains on multiplication to maintain equivalence in the fractions. Thus, this operation does not play a role in the process of finding or utilizing a common denominator.