How are common denominator and common multiple alike and different
Both common denominators and common multiples are found the same way, but a denominator is strictly on the bottom of a fraction while a multiple is not
Both common denominators and common multiples are found the same way, but a denominator is strictly on the bottom of a fraction while a multiple is not.
Explanation:
To find a common denominator of two fractions, you find a number that both denominators of the given fractions will divide into.
To find a common multiple of two numbers, you find a number that both given numbers will divide into.
This is the same process for both things. However, once you find the common denominator, you then write it in the denominator of a fraction. Once you find the common multiple, you're finished.
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this doesnt help at all
Finding a common multiple is the same as finding a common denominater
answered by answered
The concepts of common denominator and common multiple are both related to fractions and multiples, but they have distinct meanings and uses.
The common denominator is used when adding or subtracting fractions. It represents the smallest multiple that two or more denominators have in common. To find the common denominator, you need to identify the smallest number that all the denominators can divide evenly into.
Here's how you can find a common denominator:
1. Determine the denominators of the fractions you are working with.
2. Find the prime factors of each denominator.
3. Multiply the prime factors together, including any that appear more than once, to get the common denominator.
For example, if you have fractions with denominators of 4, 6, and 8, you can find the common denominator as follows:
Denominator 4 = 2 x 2
Denominator 6 = 2 x 3
Denominator 8 = 2 x 2 x 2
To find the common denominator, you multiply the prime factors together: 2 x 2 x 2 x 3 = 24
Therefore, 24 is the common denominator for 4, 6, and 8.
On the other hand, a common multiple is used when finding the least common multiple (LCM) of two or more numbers. It represents the smallest multiple that two or more numbers have in common.
To find the least common multiple (LCM), you can follow these steps:
1. Identify the numbers for which you want to find the LCM.
2. List the multiples (the multiples are obtained by multiplying each number by 1, 2, 3, and so on).
3. Look for the smallest multiple that the given numbers have in common. This is the least common multiple (LCM).
For example, to find the LCM of 4 and 6:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
From the lists above, we can see that the smallest multiple that 4 and 6 have in common is 12. Therefore, the LCM of 4 and 6 is 12.
In summary, the common denominator is used in fraction operations, identifying the smallest multiple that two or more denominators have in common. The common multiple, specifically the least common multiple (LCM), is used to find the smallest multiple that two or more numbers have in common.