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## Comment on

GCD of x and y is 12## what if the question asks for

## Hi Mohammad,

Hi Mohammad,

Then we have....

METHOD 1:

x = 12 and y = 12 meets the condition that the GCD of x and y is 12

Here, 2x = (2)(12) = 24

And 3y = (3)(12) = 36

So, the GCD of 2x and 3y = the GCD of 24 and 36

= 12

METHOD 2:

2x = (2)(2)(2)(3)(?)(?).....

3y = (3)(2)(2)(3)(?)(?).....

We can see that 2x and 3y have two 2's and one 3 in common.

So, the GCD of 2x and 3y = (2)(2)(3) = 12

Cheers,

Brent

## Hi, Brent!

What if the initial values of x and y are 12 and 24, respectively, not 12 and 12. If we need to find GCD for 2x and 2y. I got 24, not 12. What did i wrong?

Thank you in advance!

## Hi Lidiia,

Hi Lidiia,

But the correct answer IS 24 (not 12)

As long as we choose two numbers that satisfy the given condition (GCD of x and y is 12), then we will arrive at the correct answer.

12 and 24 have a GCD of 12.

So, we can let x = 12 and y = 24

We want to find the GCD for 2x and 2y

2x = (2)(12) = 24

2y = (2)(24) = 48

The GCD of 24 and 48 is 24.

Answer: D

Cheers,

Brent

## I’m sorry, I meant 2x and 3y,

## Sorry, you originally wrote

Sorry, you originally wrote "2x and 3y", but I thought it was a typo. So, I edited your question.

You're creating a different question altogether then. I believe you're asking:

If the GCD of x and y is 12, what is the GCD of 2x and 3y

In this case, there is not one unique answer. Consider these two cases.

CASE A: x = 12 and y = 12. Here, the GCD of 2x and 3y is 12

CASE B: x = 12 and y = 24. Here, the GCD of 2x and 3y is 24

Does that answer your question?

Cheers,

Brent

## Yes, that was my question.

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