The LCM of 8 and 10 is 40. There are three methods to find the LCM of two numbers: prime factorization, listing multiples, and division method. Here are the steps to find the LCM of 8 and 10 using each method:

• Prime factorization method: Write 8 and 10 as the product of prime numbers, such that; 8 = 2 × 2 × 2 and 10 = 2 × 5. Then, multiply the common and uncommon prime factors raised to their highest power, i.e. 2 × 2 × 2 × 5 = 40. Therefore, the LCM of 8 and 10 is 40.
• Listing multiples method: List the multiples of 8 and 10 separately, and then find the common multiples. The first few multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and so on. The first few multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, and so on. The common multiples of 8 and 10 are 40, 80, and so on. Therefore, the LCM of 8 and 10 is 40.
• Division method: Divide the numbers 8 and 10 by their prime factors to calculate their LCM. The product of these divisors depicts the least common multiple of 8 and 10. Divide 8 and 10 by 2, which gives 4 and 5, respectively. Then, divide 4 by 2, which gives 2. The prime factors of 8 are 2 × 2 × 2. The prime factors of 10 are 2 × 5. The LCM of 8 and 10 is the product of the prime factors raised to their highest power, i.e. 2 × 2 × 2 × 5 = 40. Therefore, the LCM of 8 and 10 is 40.

In conclusion, the LCM of 8 and 10 is 40, and it can be found using any of the three methods mentioned above.