Question

Gcd of 12 and 18 is a factor of ___ ? (a)6 (b)12(c)18 (d)36

Answer 1

`6`

Explanation:

`6`

Factors of `12: 1, 2, 3, 4, 6, 12`
Factors of `18: 1, 2, 3, 6, 9, 18`

The biggest factor they have in common is `6`, so the gcd is `6`.

Answer 2

There is a problem with the question that is asked......

Explanation:

I think you have mixed the question up.

The GCD stands for greatest common denominator.

There is no greatest .... the value could be infinitely big because it works with multiples which are infinite,

All of the following would be possibilities for a denominator.
`36,72, 108,144,180,216,252 ......`

We would usually refer to either the GCF or LCD.

The Greatest common Factor is the biggest number which divides into `12 and 18`. It is a small value.

Factors of `12:" "1,2,3,4,color(blue)(6),12`
Factors of `18:" "1,2,3,color(blue)(6),9,18`

The GCF is therefore `6`, which is a factor of all the options given in the question.

The LCD or Lowest Common Denominator is the smallest number which is divisible by `12 and 18`. It is a big number.

The multiples of `12:" "12,24,color(red)(36),48,60,72,84.......`
The multiples of `18:" "18,color(red)(36),54,72,90...`

The LCD is therefore `36` which is option (d).