# How are a common denominator and a common multiple alike and how are they different?

## (Ez one) 16 + 10=______

A. 26
B. 89
C.100
D. None of the above.

A. 43
B. 65
C. 21
D.35

## A common denominator and a common multiple are both mathematical concepts that involve numbers. However, they are used for different purposes and have distinct properties.

A common denominator is used in fraction operations, particularly when adding or subtracting fractions. It refers to a common multiple of the denominators of two or more fractions. To find a common denominator, you can follow these steps:

1. Identify the denominators of the fractions you want to operate on.
2. Find the least common multiple (LCM) of these denominators.
3. Multiply the numerators and denominators of each fraction by the necessary factor(s) to obtain a new fraction with the common denominator.

For example, consider adding the fractions 1/3 and 1/4. The denominators are 3 and 4. The LCM of 3 and 4 is 12. To make both fractions have a denominator of 12, you would multiply 1/3 by 4/4 and 1/4 by 3/3. This gives you 4/12 + 3/12 = 7/12.

On the other hand, a common multiple is used to find numbers that are divisible by two or more given numbers. It refers to a number that has multiple instances in the sequence of multiples of each individual number. To find a common multiple, you can follow these steps:

1. Determine the numbers for which you want to find a common multiple.
2. Find the multiples of each number until you find a number that appears in the list of multiples for all the given numbers.
3. This common number will be the least common multiple (LCM) of the given numbers.

For example, consider finding the common multiple of 4 and 6. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on. The multiples of 6 are 6, 12, 18, 24, 30, and so on. From these lists, we can see that 12 is the first common multiple of 4 and 6 and therefore, the LCM of 4 and 6.

In summary, a common denominator is used in fraction operations to find a common multiple of the denominators, while a common multiple is used to find a number that is divisible by multiple given numbers.