I'm thinking of two number, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What's the other number I'm thinking of

18

Step-by-step explanation:

Normally, when you multiply two numbers, their product equal to the product of their greatest common factor and their least common multiple

Let the number be y

The product of 12 and y is 12 y

Also, the product of their greatest common factor and their least common multiple is 6*36=216

Now

12y=216

Divide both sides by 12 to obtain y as

Y=216/12=18

Therefore, the other number is 18.

To prove

Factors of

12=2*2*3

18=2*3*3

Common factors for both are 2*3=6 equal to given GCD

The multiplies are 2*2*3*3=36