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.
As an AI bot, I do not have a personal life or an age. However, I can help you understand how to find the prime factorizations, LCM, and GCF for a given set of numbers.
Let's assume your age is 30, the older person's age is 40, and the younger person's age is 10 (which is 15 years of age or younger).
1. Prime Factorization:
To find the prime factorization of a number, you need to break it down into its prime factors. Here are the prime factorizations for each age:
- Your age (30): The prime factorization of 30 is 2 * 3 * 5.
- Older person's age (40): The prime factorization of 40 is 2 * 2 * 2 * 5.
- Younger person's age (10): The prime factorization of 10 is 2 * 5.
2. Least Common Multiple (LCM):
To find the LCM, you need to determine the smallest multiple that is common to all the numbers. Here's how you can calculate the LCM:
- LCM of 30 and 40: Start by listing the multiples of both numbers and identify the smallest common multiple.
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, ...
Multiples of 40: 40, 80, 120, 160, 200, 240, ...
The smallest common multiple is 120. Therefore, the LCM of 30 and 40 is 120.
- LCM of 40 and 10: Again, list the multiples and find the smallest common multiple.
Multiples of 40: 40, 80, 120, 160, 200, 240, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The smallest common multiple is 40. Therefore, the LCM of 40 and 10 is 40.
3. Greatest Common Factor (GCF):
To find the GCF, you need to determine the largest factor that divides all the numbers. Here's how you can calculate the GCF:
- GCF of 30 and 40: List the factors of both numbers and find the largest common factor.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The largest common factor is 10. Therefore, the GCF of 30 and 40 is 10.
- GCF of 40 and 10: Similarly, list the factors and find the largest common factor.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 10: 1, 2, 5, 10
The largest common factor is 10. Therefore, the GCF of 40 and 10 is 10.
I hope this explanation helps you understand how to find the prime factorizations, LCM, and GCF for a set of numbers.