CAT Word problems based on HCF and LCM - Practice Questions & MCQ

Overview:

HCF and LCM are commonly used mathematical concepts in solving word problems.
These concepts are frequently asked in management entrance exams as they test the students' problem-solving abilities.

Example Questions:

Question 1: The manager of a company wants to distribute packets of chocolates among the employees. If he wants to distribute the packets in such a way that each packet has an equal number of chocolates and there are no chocolates left, what is the minimum number of chocolates he must have?

Question 2: In a college, there are 567 students. The college wants to divide the students into different groups such that each group has the same number of students. What is the minimum number of students in each group?

Question 3: A contractor has certain lengths of wires, and he wants to cut them into equal pieces. If the lengths of the wires are 36 meters and 54 meters respectively, what is the maximum length of wire that can be obtained by cutting them into equal pieces?

Solution Approach:

Step 1: Understand the problem statement and identify the key information.

Step 2: Determine the common factors (HCF) and the least common multiple (LCM) based on the given information.

Step 3: Use the HCF or LCM to solve the problem as required. The HCF helps in finding the minimum number, while the LCM helps in finding the maximum number or quantity.

Tips and Tricks:

Tip 1: To find the HCF and LCM of two or more numbers, express them in their prime factorized form.

Tip 2: While finding the HCF, consider only the common prime factors with the lowest power.

Tip 3: While finding the LCM, consider all the prime factors with the highest powers from the given numbers.

Tip 4: For word problems, always examine the given quantities and the desired outcome, which will guide you in determining whether to use HCF or LCM.

Example Solution:

Question: The manager of a company wants to distribute packets of chocolates among the employees. If he wants to distribute the packets in such a way that each packet has an equal number of chocolates and there are no chocolates left, what is the minimum number of chocolates he must have?

Solution:

The minimum number of chocolates that the manager must have would be equal to the greatest common divisor (HCF) of the number of employees.

Given: Number of employees = 45

Prime factorization of 45: 3 * 3 * 5

Hence, the HCF of 45 is 3.

Therefore, the manager must have a minimum of 3 chocolates.

Conclusion:

Word problems based on HCF and LCM are frequently asked in management entrance exams. Understanding the problem statement carefully and applying the concepts of HCF and LCM will help in solving such problems effectively. Using prime factorization for finding HCF and LCM is a handy technique.