The LCM (Least Common Multiple) of 8 and 16 is 16. There are different methods to find the LCM of two numbers, including prime factorization, division method, and listing multiples. Here are the steps to find the LCM of 8 and 16 using each method:

• Prime Factorization Method: Write 8 and 16 as the product of prime numbers, such that; 8 = 2 × 2 × 2 and 16 = 2 × 2 × 2 × 2. The LCM of 8 and 16 is the product of the highest powers of all prime factors, which is 2 × 2 × 2 × 2 = 16.

• Division Method: Divide the numbers 8 and 16 by their prime factors to find their LCM. The product of these divisors denotes the least common multiple of 8 and 16. Divide 8 and 16 by 2, which gives 4 and 8. Divide 4 and 8 by 2, which gives 2 and 4. Divide 2 and 4 by 2, which gives 1 and 2. No more further division can be done. Thus, LCM (8, 16) = 2 × 2 × 2 × 2 = 16.

• Listing the Multiples Method: List out the multiples of 8 and 16 and find their common multiple. The first few multiples of 8 and 16 are 8, 16, 24, 32, 40, and 16, 32, 48, 64, 80, respectively. The common multiples from the multiples of 8 and 16 are 16, 32, and so on. The smallest common multiple of 8 and 16 is 16. Therefore, the LCM of 8 and 16 is 16.

In summary, the LCM of 8 and 16 is 16, and it can be found using different methods such as prime factorization, division method, and listing multiples.