Question

What is the least common denominator for `\frac{5}{12,}\frac{7}{9}`?

Answer 1

36 is the common denominator

Explanation:

You have to find the least common multiple of the denominators. This can be done by factoring each number into its prime factors.

`9=3^2`
`12=2^2*3`

We have 2 different numbers (2 and 3) so we will find the ones that have the greater exponent and multiply them.

`LCM=2^2*3^2`

`LCM=36`

Answer 2

`36`

Explanation:

For fractions with denominators up to `12`, the quickest method is to know the multiplication tables by heart.

This is a basic and essential skill in maths.

Mentally run though the multiples of the bigger number until you reach a number that is also a multiple of the other number.

Find the `LCM` of `12 and 9`

Multiples of `12` are:

`12" "larr` no, not divisible by 9.

`24" "larr` no, not divisible by 9.

`36" "larr` YES, divisible by 9! This is the LCM

For bigger numbers or for several numbers at a time, the prime factor method is better, but for two or even 3 small denominators, this is the easiest method.