The image you've provided seems to include a question related to determining the least common multiple (LCM) of a set of numbers. Here's how to solve such problems:

Problem Breakdown:

Given:

1. $a) \, 2, 4, 6, 8, 10, 12$
2. $b) \, 2, 3, 5, 6, 8, 10, 15$
3. $c) \, 3, 5, 14, 18, 25, 35, 70$

You are likely being asked to find the LCM of the entire set of numbers provided in each list.

Steps to Find the LCM:

1. List the prime factors of each number in the set.
2. Identify the highest power of each prime that appears in the factorization of any number in the list.
3. Multiply these highest powers together to find the LCM.

Solutions:

1. For Set (a): $2, 4, 6, 8, 10, 12$

   • Factorize each:
     • 2 = $2^1$
     • 4 = $2^2$
     • 6 = $2^1 \times 3^1$
     • 8 = $2^3$
     • 10 = $2^1 \times 5^1$
     • 12 = $2^2 \times 3^1$
   • LCM = $2^3 \times 3^1 \times 5^1 = 120$

2. For Set (b): $2, 3, 5, 6, 8, 10, 15$

   • Factorize each:
     • 2 = $2^1$
     • 3 = $3^1$
     • 5 = $5^1$
     • 6 = $2^1 \times 3^1$
     • 8 = $2^3$
     • 10 = $2^1 \times 5^1$
     • 15 = $3^1 \times 5^1$
   • LCM = $2^3 \times 3^1 \times 5^1 = 120$

3. For Set (c): $3, 5, 14, 18, 25, 35, 70$

   • Factorize each:
     • 3 = $3^1$
     • 5 = $5^1$
     • 14 = $2^1 \times 7^1$
     • 18 = $2^1 \times 3^2$
     • 25 = $5^2$
     • 35 = $5^1 \times 7^1$
     • 70 = $2^1 \times 5^1 \times 7^1$
   • LCM = $2^1 \times 3^2 \times 5^2 \times 7^1 = 3150$

Would you like more details or have any questions?

Here are some related questions:

1. How do you determine the greatest common divisor (GCD) of a set of numbers?
2. Can you explain how the LCM is useful in solving problems involving fractions?
3. What is the prime factorization of 3150?
4. How do you calculate the LCM if the numbers have no common factors?
5. How can LCM be applied in real-world scenarios?

Tip: Understanding how to find the LCM is particularly helpful in adding and subtracting fractions where the denominators are different.