The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that can be divided by both numbers without leaving a remainder.

To find the LCM of 9 and 18, we can use the following steps:

- List the multiples of each number:

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, … Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …

- Find the smallest multiple that is common to both lists:

The smallest multiple that is common to both lists is 36. Therefore, the LCM of 9 and 18 is 36.

Another way to find the LCM of 9 and 18 is by using the formula:

LCM(9, 18) = (9 x 18) / GCD(9, 18)

where GCD(9, 18) is the Greatest Common Divisor (GCD) of 9 and 18. Using this formula, we can calculate the LCM as follows:

LCM(9, 18) = (9 x 18) / GCD(9, 18) = 162 / 9 = 18

Note that GCD(9,18) = 9

Using prime factorization method

- Factorize the numbers into their prime factors 9 = 3^2 18 = 2*3^2
- Take the highest power of each prime factor 3^2
- Multiply all the prime factors together, it will give the LCM LCM(9, 18) = 3^2*2 = 36

In conclusion, LCM of 9 and 18 is 36. It can be calculated using different methods like listing multiples, using formula and prime factorization method.