To find the greatest common divisor (GCD) or the least common multiple (LCM) of two numbers, we can use the Euclidean algorithm.

To find the GCD of 180 and 108, we can use the following steps:

1. Divide 180 by 108: 180 ÷ 108 = 1 remainder 72
2. Divide 108 by 72: 108 ÷ 72 = 1 remainder 36
3. Divide 72 by 36: 72 ÷ 36 = 2 remainder 0

Since the remainder is 0, we stop here. The GCD of 180 and 108 is the last non-zero remainder, which is 36.

To find the LCM of 180 and 108, we can use the formula:

LCM(a, b) = (a * b) / GCD(a, b)

Using the GCD we found earlier (36), we can calculate the LCM:

LCM(180, 108) = (180 * 108) / 36 = 540

Therefore, the GCD of 180 and 108 is 36, and the LCM is 540.