A student asks about the relation between least common multiple and least common denominator. How do yourespond?
When you're adding or subtracting fractions, you need to find the least common denominator.
For instance:
1/2 + 3/4 + 5/8 = 4/8 + 6/8 + 5/8 = 15/8
The least common denominator is also the least common multiple. In the above problem that is 8.
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To understand the relationship between the least common multiple (LCM) and the least common denominator (LCD), we need to first understand what each term represents.
The LCM of two or more numbers is the smallest number that is divisible by each of the given numbers without leaving a remainder. For example, the LCM of 4 and 6 is 12 because it is the smallest number that both 4 and 6 divide evenly into.
The LCD, on the other hand, is the least common multiple of the denominators in a set of fractions. It is used in adding or subtracting fractions, where we need to find a common denominator for all the fractions involved. For example, the LCD of 1/3 and 1/4 is 12 because it is the smallest number that both 3 and 4 divide evenly into.
So, we can see that the LCM and the LCD are closely related. In fact, the LCD can be viewed as the LCM of the denominators in a set of fractions. This is because in order to find a common denominator for fractions, we need to find the smallest number that the denominators can divide into evenly, which is exactly what the LCM represents.
In summary, the LCM is the smallest number that is divisible by a set of given numbers, while the LCD is the smallest number that the denominators in a set of fractions can divide into evenly. The LCD can be seen as the LCM of the denominators.