Sure, let's tackle this step-by-step.
### Step 1: Find the Least Common Multiple (LCM)
First, we need to find the Least Common Multiple (LCM) of 20 and 40.
The LCM of two numbers is the smallest number that is a multiple of both.
For 20 and 40:
- Multiples of 20: 20, 40, 60, 80, ...
- Multiples of 40: 40, 80, 120, ...
The smallest common multiple is 40. Therefore, the LCM of 20 and 40 is 40.
### Step 2: Find the Greatest Common Divisor (GCD)
Next, we need to find the Greatest Common Divisor (GCD) of 4 and 8.
The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
For 4 and 8:
- Divisors of 4: 1, 2, 4
- Divisors of 8: 1, 2, 4, 8
The greatest common divisor is 4. Therefore, the GCD of 4 and 8 is 4.
### Step 3: Divide the LCM by the GCD
Finally, we divide the LCM found in Step 1 by the GCD found in Step 2.
[tex]\[
\frac{\text{LCM}}{\text{GCD}} = \frac{40}{4} = 10
\][/tex]
### Conclusion
Thus, when you divide the LCM of 20 and 40 by the GCD of 4 and 8, you get 10.
