Given that the least common multiple (LCM) and greatest common divisor (GCD) of two numbers are 8 and 2, we need to find the correct pair of numbers from the given options.

The product of the LCM and GCD of two numbers is equal to the product of the two numbers themselves. Mathematically, this is expressed as:

$\text{LCM} \times \text{GCD} = \text{Number 1} \times \text{Number 2}$

Given:

• LCM = 8
• GCD = 2

Therefore:

$8 \times 2 = 16$

We need to find which of the pairs of numbers in the options multiply to 16 and have a GCD of 2 and an LCM of 8.

Let's check each option:

Option (A): 14 and 16

• GCD(14, 16) = 2
• LCM(14, 16) = 112 (which is not 8)

Option (B): 6 and 24

• GCD(6, 24) = 6 (which is not 2)
• LCM(6, 24) = 24

Option (C): 20 and 48

• GCD(20, 48) = 4 (which is not 2)
• LCM(20, 48) = 240

Option (D): 2 and 8

• GCD(2, 8) = 2
• LCM(2, 8) = 8

The correct pair is Option (D): 2 and 8.

Would you like to explore this further or have any questions?

Here are 5 related questions to think about:

1. How do you calculate the GCD of two numbers using the Euclidean algorithm?
2. What is the relationship between LCM, GCD, and the product of two numbers?
3. How do you find the LCM of more than two numbers?
4. Can two numbers have the same LCM and GCD? If yes, under what conditions?
5. What are the applications of LCM and GCD in real-life situations?

Tip: When solving problems involving LCM and GCD, always check their relationship with the product of the numbers to ensure the accuracy of your calculations.