CAT HCF and LCM of fractions - Practice Questions & MCQ

Introduction to HCF and LCM of fractions

Fraction represents a part of a whole. Just like whole numbers, fractions can also have a greatest common divisor (HCF) and a least common multiple (LCM). HCF and LCM of fractions are important concepts in quantitative aptitude and are regularly asked in management entrance exams like CAT, MAT, XAT, SNAP, etc.

HCF (Highest Common Factor) of fractions

The HCF of two or more fractions is the largest fraction that can exactly divide each given fraction. To find the HCF of fractions, we need to find the HCF of the numerators and the LCM of the denominators.

Example:

Find the HCF of 2/3 and 4/9? 

Solution: The HCF of the numerators 2 and 4 is 2. The LCM of the denominators 3 and 9 is 9. Therefore, the HCF of 2/3 and 4/9 is 2/9.

LCM (Least Common Multiple) of fractions

The LCM of two or more fractions is the smallest fraction that is divisible by each of the given fractions. To find the LCM of fractions, we need to find the LCM of the numerators and the HCF of the denominators.

Example: 

Find the LCM of 1/2 and 1/3? 

Solution: The LCM of the numerators 1 and 1 is 1. The HCF of the denominators 2 and 3 is 1. Therefore, the LCM of 1/2 and 1/3 is 1/6.

Tips and Tricks for HCF and LCM of fractions

- When finding the HCF of fractions, simplify the given fractions to their lowest terms before finding the HCF of the numerators and LCM of the denominators. 

- When finding the LCM of fractions, simplify the given fractions to their lowest terms before finding the LCM of the numerators and HCF of the denominators. 

- While comparing fractions, it is convenient to have the same denominator. Find the LCM of the denominators and convert all the fractions to have the same denominator for easier comparison.

More Solved Example: 

Q1. Which fraction is greater: 3/4 or 5/6? 

Solution: 

To compare the fractions with different denominators (4 and 6), find the LCM of 4 and 6, which is 12. 

Convert 3/4 to an equivalent fraction with a denominator of 12: (3/4) x (3/3) = 9/12.

Convert 5/6 to an equivalent fraction with a denominator of 12: (5/6) x (2/2) = 10/12. Now it is easy to compare: 9/12 < 10/12. Therefore, 5/6 is greater than 3/4.

Understanding the concepts of HCF and LCM of fractions is crucial for solving quantitative aptitude questions in competitive exams. Regular practice of these concepts will help you master them and improve your problem-solving skills. Use the tips and tricks mentioned above to solve questions quickly and accurately. Remember to practise using previous year's management entrance exam questions to familiarise yourself with the exam pattern and difficulty level.