The LCM (Least Common Multiple) of 15 and 20 is 60. This means that 60 is the smallest positive integer that both 15 and 20 can divide into without a remainder. There are several methods to find the LCM of two numbers, including:

• Prime Factorization Method: Express the numbers as the product of their prime factors and then multiply the common factors raised to their highest power. For example, the prime factorization of 15 is 3 x 5 and the prime factorization of 20 is 2 x 2 x 5. The common factors are 3, 2, and 5, and the highest power of each factor is 2 x 2 x 3 x 5 = 60.

• Division Method: Write the numbers in a row and divide them by their common factors until only prime numbers are left. Then, multiply the common factors and the prime numbers. For example, divide 15 and 20 by 5 to get 3 and 4, respectively. Then, divide 3 by 3 to get 1 and leave 4 as it is. The prime factors are 3, 2, and 2, and the product is 2 x 2 x 3 x 5 = 60.

• Listing Method: List the multiples of each number until a common multiple is found. The smallest common multiple is the LCM. For example, the multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, ... and the multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180, ... The smallest common multiple is 60.

Therefore, the LCM of 15 and 20 is 60, which is the smallest positive integer that both 15 and 20 can divide into without a remainder.