Questions: Find the least common multiple (LCM) of 12 and 9.

Solution Steps

To find the least common multiple (LCM) of two numbers, we can use the relationship between the greatest common divisor (GCD) and LCM. The formula is: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] We will use Python's math module to calculate the GCD and then use the formula to find the LCM.

We are given two numbers: \(12\) and \(9\).

To find the least common multiple (LCM), we first need to calculate the greatest common divisor (GCD) of the two numbers. The GCD of \(12\) and \(9\) is \(3\).

The formula to find the LCM using the GCD is: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] Substituting the values, we get: \[ \text{LCM}(12, 9) = \frac{|12 \times 9|}{3} = \frac{108}{3} = 36 \]

Final Answer