Find the sum of all the common factors of 15 and 25.Multiply the result by the first common multiple of 3 and 7.What is the answer?

1. Break Down the Problem

1. Find the common factors of 15 and 25.
2. Calculate the sum of those common factors.
3. Determine the first common multiple of 3 and 7.
4. Multiply the sum of the common factors by the first common multiple found in the previous step.

2. Relevant Concepts

• Common factors can be found by determining the factors of each number and identifying the common ones.
• The least common multiple (LCM) of two numbers can be determined using the formula:

$\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}$

3. Analysis and Detail

Step 1: Find the common factors of 15 and 25

• Factors of 15: 1, 3, 5, 15
• Factors of 25: 1, 5, 25

Common factors: 1, 5

Step 2: Calculate the sum of the common factors

$\text{Sum} = 1 + 5 = 6$

Step 3: Determine the first common multiple of 3 and 7

• LCM(3, 7):

$\text{LCM}(3, 7) = \frac{3 \cdot 7}{\text{GCD}(3, 7)} = \frac{21}{1} = 21$

4. Verify and Summarize

• The sum of the common factors is 6.
• The first common multiple of 3 and 7 is 21.

Final Answer

$6 \times 21 = 126$

Thus, the final result is 126.