Question

Find the smallest two numbers, neither of which is 8, but their GCD is 8.

• A. 16 and 24
• B. 24 and 40
• C. 8 and 24

Answer 1

The correct option is A 16 and 24

GCD of smallest and second smallest multiple of a number is always that number.

Let's prove this mathematically.

Factorizing 8: $2\times 2\times 2$

Let's multiply $8$ with the smallest prime number, i.e., $2$.
$\Rightarrow 2\times 2\times 2\times 2=16$

This is the smallest multiple of $8$.

Now, let's multiply $8$ with the next smallest prime number, i.e., $3$.
$\Rightarrow 2\times 2\times 2\times 3=24$

This is the second smallest multiple of $8$.

GCD $(16,24)=8$

The two smallest numbers whose GCD is $8$ are $16$ and $24$.