I am 55, my motherlaw is 70, my friend is 40. How do I figure out the LCM and the GCF. My home assignment is listed as= List the ages of two people in your life, one older than you and one younger than you. It would be best if the younger person was 15 years of age or younger.
Find the prime factorizations of your age and the other two persons’ ages. Show your work listed by name and age. Make sure your work is clear and concise.
Find the LCM and the GCF for each set of numbers. Again, be clear and concise. Explain or show how you arrived at your answers.
In your own words, explain the meaning of your calculated LCM and GCF for the ages you selected. Do not explain how you got the numbers; rather explain the meaning of the numbers. Be specific to your numbers; do not give generic definitions.
Respond to at least two of your classmates’ postings. Did your classmates calculate the LCM and GCF correctly? Are their interpretations correctly applied to the ages?
FACTORS
GCF <= 40.
1 * 70 = 70
2 * 35 = 70
5 * 14 = 70
7 * 10 = 70
1 * 55 = 55
5 * 11 = 55
1 * 40 = 40
2 * 20 = 40
4 * 10 = 40
5 * 8 = 40
GCF = 5.
LCM =>70
Limit max. value to:70*55*40= 154000.
These numbers are very hard to work
with. I did this mostly by trial and error:
2 * 70 = 140
3 * 70 = 210
30 * 70 = 2100
40 * 70 = 2800
44 * 70 = 3080. This # is divisible
by 70, 55, and 40. It is the smallest
i could find.
LCM = 3080.
To figure out the LCM (Least Common Multiple) and the GCF (Greatest Common Factor), you need to follow these steps:
1. Identify the ages of the three people: you (55), your mother-in-law (70), and your friend (40).
2. To find the prime factorizations of each age, you'll need to break down the numbers into their factors. Start by dividing the number by the smallest prime number (2) and continue dividing until you can't divide anymore.
3. Let's start with your age, 55:
- Divide 55 by 2 → 27 remainder 1
- Divide 27 by 3 → 9 remainder 0
- Divide 9 by 3 → 3 remainder 0
- Divide 3 by 3 → 1 remainder 0
The prime factorization of 55 is 5 x 11, as there are no more factors left.
4. Next, let's find the prime factorization for your mother-in-law's age, 70:
- Divide 70 by 2 → 35 remainder 0
- Divide 35 by 5 → 7 remainder 0
The prime factorization of 70 is 2 x 5 x 7.
5. Finally, let's find the prime factorization for your friend's age, 40:
- Divide 40 by 2 → 20 remainder 0
- Divide 20 by 2 → 10 remainder 0
- Divide 10 by 2 → 5 remainder 0
The prime factorization of 40 is 2 x 2 x 2 x 5.
Now that we have the prime factorizations for each age, we can move on to finding the LCM and GCF.
6. To find the LCM, you need to understand that it represents the smallest multiple that all the numbers have in common. To find it, you need to list out all the factors and their highest powers from the prime factorizations:
- The prime factors for 55 are 5 (power 1) and 11 (power 1).
- The prime factors for 70 are 2 (power 1), 5 (power 1), and 7 (power 1).
- The prime factors for 40 are 2 (power 3) and 5 (power 1).
To calculate the LCM, you multiply all the factors together with the highest powers:
LCM = 2^3 x 5^1 x 7^1 x 11^1 = 2 x 2 x 2 x 5 x 7 x 11 = 3,080.
7. To find the GCF, you need to understand that it represents the largest factor that all the numbers have in common. To calculate it, you identify the common prime factors and use the lowest power for each:
- The common prime factors are 2 (power 1) and 5 (power 1).
To calculate the GCF, you multiply the common prime factors with the lowest power:
GCF = 2^1 x 5^1 = 2 x 5 = 10.
Now, to explain the meaning of the calculated LCM and GCF:
The LCM (3,080) represents the smallest age at which all three people (you, your mother-in-law, and your friend) will have the same multiple of their ages. In other words, if we were to fast-forward time until everyone reached a certain age, that age would be 3,080.
The GCF (10) represents the highest common factor that all three ages share. It's the largest number you can divide evenly into each age, indicating the largest potential factor that could represent a common event, such as a celebration, anniversary, or any other occasion where the ages align.
In responding to your classmates' postings, you should evaluate if they calculated the LCM and GCF correctly by reviewing their step-by-step process. Verify if they correctly identified the prime factorizations and applied the correct powers for each prime factor. Additionally, assess if their interpretations of the LCM and GCF for their selected ages accurately reflect the significance of those numbers given their context.