All numbers in our real number system are the product of prime numbers. Complete the following steps for this discussion:
1. 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.
1. Nancy – my mom is 60
2. Hali – my niece is 8
3. Tammy – my age is 40
2. 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.
1. My mom is 60 and 60 is not a prime number. The prime factorizations for my mom are 2x2x3x5=60.
2. My niece is 8 and 8 is not a prime number. The prime factorizations for my niece are 2x2x2=8.
3. My age is 40 and 40 is not a prime number. The prime factorizations for my age are 2x2x2x5=40.
3. 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.
I do not know how to do number 3...
Least common multiple is the smallest number that is divisible by all three numbers.
LCM: 60, 40, 8 = 120
The greatest common factor is the largest number that goes into all three numbers.
GCF: 60, 40, 8 = 4
http://www.mathsisfun.com/greatest-common-factor.html
http://www.mathsisfun.com/least-common-multiple.html
Thank you Ms. Sue
You're welcome, Tammy.
No problem! Let's go through the steps to find the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) for each set of numbers.
To find the LCM:
1. Take the prime factorizations of the numbers.
2. Identify the highest power of each prime factor that appears in any of the factorizations.
3. Multiply all the prime factors, each raised to the highest power identified.
To find the GCF:
1. Take the prime factorizations of the numbers.
2. Identify the lowest power of each prime factor that appears in any of the factorizations.
3. Multiply all the prime factors, each raised to the lowest power identified.
Let's apply this to the ages given:
1. Nancy (60):
Prime factorization: 2 x 2 x 3 x 5 = 60
2. Hali (8):
Prime factorization: 2 x 2 x 2 = 8
3. Tammy (40):
Prime factorization: 2 x 2 x 2 x 5 = 40
Now, let's find the LCM and GCF for each set:
For Nancy (60) and Hali (8):
LCM: 2 x 2 x 2 x 3 x 5 = 120
GCF: 2 x 2 = 4
For Nancy (60) and Tammy (40):
LCM: 2 x 2 x 2 x 3 x 5 = 120
GCF: 2 x 2 = 4
For Hali (8) and Tammy (40):
LCM: 2 x 2 x 2 x 3 x 5 = 120
GCF: 2
So, the LCM for all three sets of ages is 120, and the GCF for each set is as follows:
- Nancy (60) and Hali (8): GCF = 4
- Nancy (60) and Tammy (40): GCF = 4
- Hali (8) and Tammy (40): GCF = 2