Questions: Question 8 Find the least common multiple of 90 and 54. Add your answer Integer, decimal, or E notation allowed

Solution Steps

To find the least common multiple (LCM) of two numbers, we can use the relationship between the greatest common divisor (GCD) and the 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.

To find the least common multiple (LCM) of \(90\) and \(54\), we first need to calculate the greatest common divisor (GCD). The GCD of \(90\) and \(54\) is given by: \[ \text{GCD}(90, 54) = 18 \]

Using the relationship between the GCD and LCM, we can calculate the LCM using the formula: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \] Substituting the values we have: \[ \text{LCM}(90, 54) = \frac{|90 \times 54|}{18} \]

Calculating the product: \[ 90 \times 54 = 4860 \] Now, substituting this back into the LCM formula: \[ \text{LCM}(90, 54) = \frac{4860}{18} = 270 \]

Final Answer