Barstow Community College Finding the Least Common Multiple Discussion

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User Generated

User

Sena213

Subject

Mathematics

School

Barstow Community College

Description

This discussion has two parts:

1. Discuss and explain how you would go about finding the Least Common Denominator of a set of numbers and provide an example where you find the least common denominator between two numbers. (17 points)

2. Reply to all of your classmates' posts, providing questions, suggestions, help, and enough feedback to elaborate on your post/reply. ( 8 points)

---------------------------------------------------------------- respond to these posts----------

Tiffany,

Example: What is 1/6 + 7/15The Denominators

The Denominators are 6 and 15:

Then the Least Common Multiple of 6 and 15 is 30.

Multiples of 6: 6,12,18,24,30,36, …

Multiples of 15: 15, 30, 45, 60, …

Now let's try to make the denominators the same.

Note: what we do to the bottom of the fraction,
we must also do to the top

For the first fraction we can multiply top and bottom by 5 to get a denominator of 30:

1 multiply 5 = 5

6 multiply 5 = 30

1/6 = 5/30

For the second fraction we can multiply top and bottom by 2 to get a denominator of 30:

7 multiply 2 = 14

15 multiply 2 = 30

7/15 = 14/30

Now we can do the addition by adding the top numbers:

5/30 + 14/30

The fraction is already as simple as it can be, so that is the answer.

= 19/30

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Carlo,

Hello Professor and Classmates,

To find the Least Common Denominator or LCD of two sets of numbers, we have to find their prime numbers.

My example:

$LaTeX: \frac{3}{6}+\frac{2}{15}$ 3 6 + 2 15

The denominators are 6 and 15. Now their LCD

$LaTeX: 6=2\cdot3$ 6 = 2 ? 3

$LaTeX: 15=\:\:\:3\cdot5$ 15 = 3 ? 5

Now bring the numbers down, 3 occurs on both numbers, so let us only write one of them, 2,3,5 and then multiply them to each other and you will get $LaTeX: 2\cdot3\cdot5=30$ 2 ? 3 ? 5 = 30 .

Now $LaTeX: \frac{3}{6}+\frac{2}{15}$ 3 6 + 2 15 , becomes, $LaTeX: \frac{3}{30}+\frac{2}{30}$ 3 30 + 2 30

Next step, let us add the numerators LaTeX: 3+2=5 3 + 2 = 5 , and bring down the LCD which will give us , $LaTeX: \frac{5}{30}$ 5 30 . We can factor 5 out of both 5 and 30, how many 5s we get from 5 is 1, and how many 5s we get from 30 is 6, now lets rewrite it, and this will give us the answer of $LaTeX: \frac{1}{6}$ 1 6 .

This is my understanding. Please feel free to correct me if I'm wrong, thank you.

Tags: Greatest Common Factor Least common multiple Least Common Denominator The greatest common factor The Denominators

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Explanation & Answer

Please find attached the answer...

Discussion:
The example for finding the Least Common Multiple of the following :
4/6 and 3/8
The denominators are 6 and 8. Let us write the multiples of each:
6- 12, 18,24, 30, 36, 42, 48
8- 16, 24, 32, 40, 48
The first common number that occurs in both the sets is 24. So, 24 is the LCM.
But listing common multiples for very large numbers can be challenging. So, the product of those
numbers can be divided bby their Greatest Common Factor (GCF).
7/12 and 3/15
The greatest common factor of 12 and 15 is 3
So, inorder to find the LCM, It is a good ...