Kate ate 1/3 part of the ice-cream and her sister ate 1/2 of the ice-cream. The fraction of the ice-cream was eaten by both sisters is__________.

The correct answer is:

Step1: First we will write all the fractions and then we will write the denominator and then we will use prime factorization method to add the fraction.
Fractions are:  and 
In this question the denominators are  and .
Factors of  are:
Factors of  are:
Step2:  For calculating the LCM we will multiply the factors by considering the common factors only one time with the highest exponent.
In this case there is no common factor so we will multiply all the factors.
LCM (,) = 
LCM (,) = 
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
So, 
and 
So, we will multiply the numerator of  by  and numerator of  by .

So, they both ate a total of  of ice-cream.