Fraction simplification Rules

I am studying for GRE and One of the practice questions is a division. After converting my Mixed numeral I get $\frac{90}{72}$ now I just have to simplify.

What I understood is that you divide by Least common multiplier so I

$1.)$ Divide $\frac{90}{72}$ by $2$: And I got $\frac{45}{36}$

$2.)$ Divide $\frac{45}{36}$ by $3$: And I got $\frac{9}{12}$

$3.)$ and so on until I got to 3/4 which is the wrong answer

If in step $1$, I would have divide by $3$

$1.)$ Divide $\frac{90}{72}$ by $3$ and I got $\frac{10}{8}$ $2.)$ Divide $\frac{10}{8}$ by $2$ and I got \frac{5}{4} which is the right answer

What is the rule to simplify fractions?

• You divided 45 by 3 and got 9? – user296602 Apr 27 '16 at 4:46
• 45 divided by 3 is 15 not 9, that's why this question is even here :) – KKZiomek Apr 27 '16 at 4:49
• Not divided by LCM. But by HCF. – N.S.JOHN Apr 27 '16 at 16:37

You have $\frac{90}{72}$.Now,$\gcd(90,72)=18$.
So,dividing numerator and denominator by $18$ we get $\frac{5}{4}.$