What is the least common denominator (LCD)?

What is the least common denominator (LCD)?

• A. The smallest common multiple of the denominators
• B. The largest common multiple
• C. The smallest integer that is a common multiple of the given integers
• D. The sum of the denominators

Answer: (C)

The LCD is the smallest positive number that all the denominators divide into evenly. In other words, the least common multiple of the denominators. This number lets you rewrite fractions so they have the same bottom, which is essential for adding or subtracting them. For example, with denominators 3 and 4, the LCD is 12, because 12 is divisible by both 3 and 4, and no smaller positive number works. The largest common multiple wouldn’t serve as a shared denominator, since it’s the opposite of what we need. And the sum of the denominators has nothing to do with aligning fractions, so it can’t be the LCD.

The LCD is the smallest positive number that all the denominators divide into evenly. In other words, the least common multiple of the denominators. This number lets you rewrite fractions so they have the same bottom, which is essential for adding or subtracting them. For example, with denominators 3 and 4, the LCD is 12, because 12 is divisible by both 3 and 4, and no smaller positive number works.

The largest common multiple wouldn’t serve as a shared denominator, since it’s the opposite of what we need. And the sum of the denominators has nothing to do with aligning fractions, so it can’t be the LCD.