LCM & Meatloaf: Solving Tom's Problem

• MHB
• Acesoar
In summary, Tom is making meatloaf with 3/4 pound of turkey and 5/6 pound of beef. The LCM he should use to find the total number of pounds of meat is 12. This is found by finding the GCD of the denominators (2) and then multiplying the denominators together and dividing by the GCD. To convert the fractions to equivalent fractions with a denominator of 12, we can multiply each fraction by 1 in the form of n/n, where n is the LCD divided by the denominator of the fraction. Asking for help is always a great way to learn and understand math concepts better.
Acesoar
Question: Tom is making meatloaf with 3/4 pound of turkey and 5/6 pound of beef. What is the LCM he should use to find the total number of pounds of meat?

I keep getting 15/2 or 7 & 1/2, I'm not sure how to check this though and I'm also not sure how I use that answer to find the total pounds of meat? Any help would be greatly appreciated, Thank you.(Not sure if I'm in the right section, and this might be an extremely easy problem to many of you, but I am a father and my daughter is in 6th grade and and at this time of the night I got frustrated to the point that I needed to vent and trying to get some help solving this is helping me with that, lol)

Acesoar said:
Question: Tom is making meatloaf with 3/4 pound of turkey and 5/6 pound of beef. What is the LCM he should use to find the total number of pounds of meat?

12 is the LCM use as the common denominator. Do you see why?

I know the LCD is 12, but I thought that the LCM of a fraction is LCM/HCF?

Acesoar said:
Question: Tom is making meatloaf with 3/4 pound of turkey and 5/6 pound of beef. What is the LCM he should use to find the total number of pounds of meat?

I keep getting 15/2 or 7 & 1/2, I'm not sure how to check this though and I'm also not sure how I use that answer to find the total pounds of meat? Any help would be greatly appreciated, Thank you.

I would first look at the prime factorization of both denominators:

$$\displaystyle 4=2\cdot2$$

$$\displaystyle 6=2\cdot3$$

We see that the greatest common divisor (GCD) or greatest common factor is 2.

And so the LCD will be the product of the denominators divided by the GCD

$$\displaystyle \text{LCD}=\frac{4\cdot6}{2}=12$$

Now, you want to multiply each fraction by 1 in the form:

$$\displaystyle 1=\frac{n}{n}$$

where $n$ is the LCD divided by the denominator in the fraction you are converting. Can you use this method to convert each fraction to an equivelent fraction having a denominator of 12?

Acesoar said:
(Not sure if I'm in the right section, and this might be an extremely easy problem to many of you, but I am a father and my daughter is in 6th grade and and at this time of the night I got frustrated to the point that I needed to vent and trying to get some help solving this is helping me with that, lol)

You posted in the correct forum, and you showed what you've tried, so you did well. There are problems that each of us here would find humbilng, so we don't tend to look at a problem and say, "Oh, that's easy...why are they asking for help?"

Acesoar said:
Question: Tom is making meatloaf with 3/4 pound of turkey and 5/6 pound of beef. What is the LCM he should use to find the total number of pounds of meat?

I keep getting 15/2 or 7 & 1/2, I'm not sure how to check this though and I'm also not sure how I use that answer to find the total pounds of meat? Any help would be greatly appreciated, Thank you.(Not sure if I'm in the right section, and this might be an extremely easy problem to many of you, but I am a father and my daughter is in 6th grade and and at this time of the night I got frustrated to the point that I needed to vent and trying to get some help solving this is helping me with that, lol)

That is what we are here for! Everyone here, I am sure, has some inadequacy with a certain type of math. I know I do, so the best way to get help is to ask a question with the information you know. Great Job asking the question, and even better job helping your daughter and caring about education. We are here to help, not just give answers; we all want everyone to understand the process.

Thanks for posting!

1. What is LCM and how is it used in solving Tom's problem?

LCM stands for Least Common Multiple. It is the smallest positive integer that is divisible by two or more given numbers. In solving Tom's problem, LCM is used to find the smallest number of meatloaf and cupcakes that can be made to satisfy the given constraints.

2. What are the steps involved in using LCM to solve Tom's problem?

The steps involved in using LCM to solve Tom's problem are:

1. Identify the given numbers (in this case, the number of meatloaf and cupcakes needed).
2. List the multiples of each number.
3. Find the smallest multiple that is common to both numbers.
4. This smallest multiple is the LCM, and it represents the minimum number of meatloaf and cupcakes needed to satisfy the given constraints.

3. How does the concept of LCM relate to real-life situations?

LCM is a useful concept in real-life situations where we need to find the minimum number of items to satisfy a given constraint. For example, if we need to buy enough ingredients to make a certain number of dishes, LCM can help us determine the minimum amount of each ingredient we need to purchase.

4. Can LCM be used with more than two numbers?

Yes, LCM can be used with more than two numbers. The steps involved in finding the LCM remain the same, but you would need to list the multiples of all the given numbers and find the smallest multiple that is common to all of them.

5. Are there any other methods that can be used to solve Tom's problem, besides using LCM?

Yes, there are other methods that can be used to solve Tom's problem, such as finding the common factors of the given numbers and dividing them by the highest common factor. However, using LCM is the most efficient and straightforward method for solving this type of problem.

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