All numbers in our real number system are the product of prime numbers. Complete the following steps for this discussion:
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?
As an AI, I don't have personal experiences or relations, so I cannot provide specific ages of people in my life. However, I can explain the steps to find prime factorizations, LCM, and GCF using a hypothetical example.
Let's say your age is 28, and the younger person's age is 12.
1. Prime Factorization:
To find the prime factorizations, we need to break down each number into its prime factors.
- Your age (28):
The prime factorization of 28 can be found by dividing it by prime numbers until we can no longer divide.
28 ÷ 2 = 14
14 ÷ 2 = 7
So, the prime factorization of 28 is 2 x 2 x 7, represented as 2² x 7.
- Younger person's age (12):
12 ÷ 2 = 6
6 ÷ 2 = 3
So, the prime factorization of 12 is 2 x 2 x 3, represented as 2² x 3.
2. LCM (Least Common Multiple):
The LCM is the smallest multiple that both numbers share. To find it, we need to list the multiples of each number and find the least common one.
Multiples of 28: 28, 56, 84, 112, ...
Multiples of 12: 12, 24, 36, 48, ...
From the list, we can see that the least common multiple is 84.
3. GCF (Greatest Common Factor):
The GCF is the largest factor that both numbers have. To find it, we need to list the factors of each number and find the greatest common one.
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 12: 1, 2, 3, 4, 6, 12
From the list, we can see that the greatest common factor is 4.
4. Interpretation of LCM and GCF:
The LCM (84) represents the smallest age at which both you and the younger person would have a birthday at the same time. It is the least common multiple of your ages.
The GCF (4) represents the largest common factor/divisor that can evenly divide both ages. It reflects the maximum number of whole years that can evenly go into both ages.
Please note that these are hypothetical numbers and interpretations. For the actual ages provided by your classmates, you'll need to apply the steps and interpret the results accordingly.
Remember to respond to your classmates' postings and assess whether they calculated the LCM and GCF correctly and if their interpretations are accurately applied to the ages.