# Question: GCD of x and y is 12

## Comment on GCD of x and y is 12

### what if the question asks for

what if the question asks for 3y not 2y? 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!

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? ### 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.

Cheers,
Brent

### I’m sorry, I meant 2x and 3y,

I’m sorry, I meant 2x and 3y, but with 12 and 24 instead of 12 and 12. ### 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