To find the Least Common Multiple (LCM) of 3 and 8, we can use the formula that relates the LCM and the Greatest Common Divisor (GCD) of two numbers:
[tex]\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \][/tex]
Here, [tex]\( a = 3 \)[/tex] and [tex]\( b = 8 \)[/tex].
Step 1: Find the GCD of 3 and 8.
The GCD (Greatest Common Divisor) of two numbers is the largest number that divides both of them without leaving a remainder. For the numbers 3 and 8, the only common divisor is 1 since 3 is a prime number and 8 is a power of 2. Therefore,
[tex]\[ \text{GCD}(3, 8) = 1 \][/tex]
Step 2: Calculate the product of 3 and 8.
[tex]\[ |3 \times 8| = 24 \][/tex]
Step 3: Use the LCM formula.
[tex]\[ \text{LCM}(3, 8) = \frac{|3 \times 8|}{\text{GCD}(3, 8)} \][/tex]
Since the GCD of 3 and 8 is 1,
[tex]\[ \text{LCM}(3, 8) = \frac{24}{1} = 24 \][/tex]
So, the LCM of 3 and 8 is 24.
