Question

use the following information to answer questions 1 and 2.

a and b below represent two numbers with the following prime factorizations:

\\a = 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7\\
\\b = 2 \cdot 3 \cdot 3 \cdot 7\\

1. what is the greatest common factor of these two numbers, a and b?

1. what is the least common multiple of these two numbers, a and b?

Explanation:

Identify the prime factorizations

Using the Prime Factorization knowledge point

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Find the greatest common factor (GCF)

Using the Greatest Common Factor knowledge point

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Find the least common multiple (LCM)

To find the least common multiple (LCM) of two numbers from their prime factorizations, we take the highest power of each prime number that appears in either factorization.

Comparing the exponents of each prime factor:

• For \(2\): the highest power is \(2^2\)
• For \(3\): the highest power is \(3^2\)
• For \(5\): the highest power is \(5^2\)
• For \(7\): the highest power is \(7^1\)

Now, we multiply these highest powers together:

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Answer:

Question 1

42

Question 2

6300