Let's determine the lowest common multiple (LCM) of the numbers 24 and 108 using the following steps:
1. Find the Greatest Common Divisor (GCD):
To find the LCM, we first need to determine the greatest common divisor (GCD) of 24 and 108. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
After determining the GCD of 24 and 108, we get:
[tex]\[
\text{GCD}(24, 108) = 12
\][/tex]
2. Use the GCD to Find the LCM:
The formula for the least common multiple in terms of the GCD is:
[tex]\[
\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}
\][/tex]
Here, [tex]\(a = 24\)[/tex] and [tex]\(b = 108\)[/tex].
3. Calculate the Product of the Numbers:
Let's calculate the product of 24 and 108:
[tex]\[
24 \times 108 = 2592
\][/tex]
4. Divide the Product by the GCD:
Now, we divide this product by the GCD we found earlier:
[tex]\[
\text{LCM}(24, 108) = \frac{2592}{12}
\][/tex]
5. Perform the Division:
Carry out the division to get the LCM:
[tex]\[
\frac{2592}{12} = 216
\][/tex]
Therefore, the lowest common multiple of 24 and 108 is:
[tex]\[
\boxed{216}
\][/tex]
