Questions: Find the least common multiple of 4 and 9. Now list the prime factorization of 9 using exponential notation. 9=3^2

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 LCM of two numbers \(a\) and \(b\) can be found using the formula: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \]

For the prime factorization of 9, we can directly state that \(9 = 3^2\).

To find the least common multiple (LCM) of \(4\) and \(9\), we first need to calculate the greatest common divisor (GCD) of these two numbers. The GCD of \(4\) and \(9\) is \(1\) because they have no common prime factors.

The relationship between the LCM and GCD of two numbers \(a\) and \(b\) is given by: \[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \]

Using the formula: \[ \text{LCM}(4, 9) = \frac{|4 \times 9|}{\text{GCD}(4, 9)} = \frac{36}{1} = 36 \]

The prime factorization of \(9\) is: \[ 9 = 3^2 \]

Final Answer