Final Answer:
The GCD and LCM of the given pair of natural numbers, 66 and 88, is 22 and 264, respectively.
Step-by-step explanation:
To find the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two numbers, 66 and 88, we can follow these steps:
**Greatest Common Divisor (GCD):**
1. List the factors of each number.
2. Identify the highest factor that appears in both lists.
Let's find the factors:
For 66:
1, 2, 3, 6, 11, 22, 33, 66
For 88:
1, 2, 4, 8, 11, 22, 44, 88
The common factors of 66 and 88 are:
1, 2, 11, and 22
Out of these, the highest common factor is 22, which means the GCD of 66 and 88 is 22.
**Least Common Multiple (LCM):**
The LCM of two numbers is the smallest multiple that is exactly divisible by both numbers.
There's a relationship between the LCM and GCD of two numbers, which is given by the formula:
LCM (a, b) = (a*b) / GCD
Using this formula and the GCD we found, we can calculate the LCM.
For 66 and 88:
LCM (66, 88) = 66*88 / 22
First, calculate the product of the two numbers:
66*88 = 5808
Next, divide by the GCD we found, which is 22:
5808/22 = 264
So the LCM of 66 and 88 is 264.
In summary, the GCD of 66 and 88 is 22, and the LCM is 264.