Find the sum of all the common factors of 8 and 52.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 8 and 52.
2. Calculate the sum of the common factors.
3. Find the first common multiple of 3 and 7.
4. Multiply the sum of the common factors by the first common multiple.

2. Relevant Concepts

• Common factors are numbers that can divide both numbers without a remainder.
• The least common multiple (LCM) is the smallest positive integer that is a multiple of both numbers.

3. Analysis and Detail

Step 1: Find the common factors of 8 and 52.

• Factors of 8: $1, 2, 4, 8$
• Factors of 52: $1, 2, 4, 13, 26, 52$
• Common factors: $1, 2, 4$

Step 2: Calculate the sum of the common factors.

$\text{Sum} = 1 + 2 + 4 = 7$

Step 3: Find the first common multiple of 3 and 7.

The multiples of 3 are: $3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, \ldots$

The multiples of 7 are: $7, 14, 21, 28, 35, 42, \ldots$

The first common multiple is $21$.

Step 4: Multiply the sum of the common factors by the first common multiple.

$\text{Result} = 7 \times 21 = 147$

4. Verify and Summarize

• Common factors of 8 and 52: $1, 2, 4$
• Sum of common factors: $7$
• First common multiple of 3 and 7: $21$
• Final computation: $7 \times 21 = 147$

Final Answer

The final result is $147$.