Many people use the phrase least common denominator to describe something as being base or common. It connotes something that appeals to most people, something that we all value. It is the intersection of what we all value, in the set-theory sense. But in arithmetic the LCD is the union of the prime factors of the denominators (including the multiplicity of those factors).
Perhaps greatest common divisor is a better metaphor for what is typically described as an LCD, the GCD being the intersection of prime factors.