The term "least common denominators" refers to a mathematical concept related to fractions and their common multiples. It is the smallest number that can be evenly divided by the denominators of two or more fractions.
In mathematics, a fraction consists of a numerator (the top number) and a denominator (the bottom number), separated by a slash. The denominator represents the total number of equal parts the whole is divided into, while the numerator represents the quantity of those parts being considered. Fractions can have different denominators, making it difficult to directly compare or perform arithmetic operations on them.
To solve this problem, finding the least common denominator (LCD) becomes necessary. The LCD is the smallest multiple that all the denominators can evenly divide. By finding the LCD, the fractions can be rewritten with the same denominators, allowing for easy comparison, addition, subtraction, or multiplication.
For example, let's say we have the fractions 1/4 and 2/5. The denominators are 4 and 5. The multiples of 4 are 4, 8, 12, 16, ... and the multiples of 5 are 5, 10, 15, 20, ... The smallest common multiple of 4 and 5 is 20. Therefore, the least common denominator of 1/4 and 2/5 is 20. We can rewrite the fractions as 5/20 and 8/20.
In summary, the least common denominators refer to the smallest common multiple of two or more denominators of fractions, allowing for easy comparison and mathematical operations.
