The LCM (Least Common Multiple) of 10 and 15 is 30. The LCM of any two numbers is the smallest positive integer that is divisible by both numbers with no remainder. There are different methods to find the LCM of two numbers, including prime factorization, division method, and listing the multiples. Here are the steps to find the LCM of 10 and 15 using the different methods:

• Prime Factorization Method: Find the prime factors of each number and multiply the highest power of each factor. The prime factors of 10 are 2 and 5, and the prime factors of 15 are 3 and 5. The highest power of 2 is 1, the highest power of 3 is 1, and the highest power of 5 is 1. Therefore, LCM of 10 and 15 is 2 x 3 x 5 = 30.

• Division Method: Divide the larger number by the smaller number and find the remainder. Then, divide the smaller number by the remainder and find the remainder. Continue this process until the remainder is zero. The last divisor is the LCM. For example, divide 15 by 10 to get a remainder of 5. Then, divide 10 by 5 to get a remainder of 0. Therefore, the LCM of 10 and 15 is 5 x 2 = 10.

• Listing the Multiples: List the multiples of each number until you find a common multiple. The first few multiples of 10 are 10, 20, 30, 40, 50, 60, 70, and so on. The first few multiples of 15 are 15, 30, 45, 60, 75, 90, 105, and so on. The common multiples of 10 and 15 are 30, 60, 90, and so on. Therefore, the LCM of 10 and 15 is 30.

In summary, the LCM of 10 and 15 is 30, which can be found using different methods such as prime factorization, division method, and listing the multiples.