CAT Quantitative Aptitude HCF & LCM: Basics, Calculation Process, Formulas and Solved Questions

CAT HCF and LCM is considered as one of the easiest topics by test takers. Not more than 1 question can be expected from this HCF and LCM topic in CAT Question Paper. However, knowing the right formulas and basic concepts of HCF and LCM can help in scoring +3 marks. The questions asked from the topic will be objective type and could be in the form of long statements or without numbers. For example, the question should be like find the LCM of a – b and b. Check CAT QA Syllabus

Read the article to know more about the basic concepts, important formula and solved sample questions to get an idea about the type of questions that can be asked from this topic in CAT 2021. 

What is HCF or Highest Common Factor?

In Mathematics, HCF or Highest Common Factor is considered as the most known greatest common divisor of two or more positive integers that are the reasons for the division of the numbers without leaving a remainder. 

• As an example two numbers i.e 8 and 12 are taken. 
• The H.C.F. of these two numbers i.e 8 and 12 is 4 as this is the highest number that can divide both the numbers. 
• By using a factor tree, HCF of any number can be calculated. 

How to Calculate HCF? - HCF is calculated by using some process or methods that are listed below.

• Factorization Method
• Prime Factorization Method
• Division Method

HCF Prime Factorisation Method

To explain HCF Prime Factorisation Method, the HCF of 144, 104 and 160 are given with solution

• The prime factors of 144, 104 and 160.
• 144 = 2 × 2 × 2 × 2 × 3 × 3
• 104 = 2 × 2 × 2 × 13
• 160 = 2 × 2 × 2 × 2 × 2 × 5
• The common factors of 144, 104 and 160 are 2 × 2 × 2 = 8
• So, HCF (144, 104, 160) = 8

HCF Division Method

• To explain the HCF Division Method, the HCF of 144 and 160 are mentioned.
• As 160>144, therefore the dividend = 160 and the divisor = 144.
• Here, 16 is the highest number that divides 160 and 144.
• So, HCF (144, 160) = 16

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What is LCM or Least Common Multiple?

In arithmetic, LCM or Least Common Multiple can be defined as the least number that is divisible by two or more than two numbers. For example, 4 and 6 are taken as two numbers.

• Multiples of 4 are: 4,8,12,16,20,24…
• Multiples of 6 are: 6,12,18,24….
• The common multiples for both 4 and 6 are 12,24,36,48…. Here, LCM will be 12.
• On the other side, LCM of 24 and 15 will be 2 × 2 × 2 × 3 × 5 = 120

LCM Prime Factorisation Method

To explain LCM Prime Factorisation Method, the LCM of 60 and 45 are given with solution

• Prime Factorisation of 60 and 45
• 60 = 2 × 2 x 3 × 5
• 45 = 3 × 3 × 5
• LCM = 2 × 2 x 3 × 3 × 5 = 180

LCM Division Method

To explain LCM Division Method, the LCM of 60 and 45 are given with solution

• Division of 60 and 45
• LCM of 60 and 45 = 2 × 2 x 3 × 3 × 5 = 180

CAT Quantitative Aptitude: HCF and LCM Important Formulas 

In the section below, formulas regarding HCF and LCM are mentioned.

Product of Two numbers = (HCF of the two numbers) x (LCM of the two numbers)

If A and B are taken as the numbers the formula will be A x B = H.C.F.(A,B) x L.C.M.(A,B)

CAT Quantitative Aptitude HCF and LCM Solved Questions

In the section below, some solved questions of CAT HCF and LCM are given.

Ques. Find out the number of pairs of integers (x, y) stays for the product of x, y and HCF (x, y) = 1080.

1. 8
2. 7
3. 9
4. 12

Correct Answer: ( 3)

Ques. What are the pairs of positive integers x, y remains for HCF of x, y = 35 and sum of x and y = 1085?

1. 12
2. 8
3. 15
4. 30

Correct Answer: ( 3)

Ques. Calculate the pairs of positive integers x, y remaining to get HCF (x, y) + LCM (x, y) = 91?

1. 10
2. 8
3. 6
4. 7

Correct Answer: ( 2)

Ques. If the total of two numbers i.e x, y = 1050 find out the maximum value of the HCF between x and y

1. 350
2. 700
3. 1050
4. 525

Correct Answer: ( 4)

Ques. What are the possible pairs can be found when the total of two non co–prime numbers added to their HCF and come out with 91. How many such pairs are possible?

1. 2
2. 4
3. 3
4. 6

Correct Answer: ( 3)

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Ques. When a > b, HCF (a, b) = h and LCM (a, b) = l. Find out the LCM of a – b and b

1. l
2. (a - b) b
3. (a - b) b / h
4. h (a - b)

Correct Answer: ( 3)

Ques.In every minute, a red light flashes 3 times whereas a green light sparks 5 times in 2 minutes at regular intervals. Find out the number of times both the light flashes together in each hour when the timing of their flashing is the same. 

1. 30
2. 24
3. 20
4. 60 

Correct Answer: ( 1)

Ques. After dividing by 2,3,4,5,6, A is taken as the positive integer. And the outcome of the division remains 1,2,3,4,5 respectively. What are the number of integers from 0 to 100 that belong to the set A?

1. 0
2. 1
3. 2
4. None of these

Correct Answer: ( 2)

Ques.There are 6 virtual stripes containing some or all the colours of yellow, green, blue and red in a new flag. How many ways it can be designed so that no 2 adjucent stripes contain the same colour?

1. 12 × 81 
2. 16 × 192 
3. 20 × 125 
4. 24 × 216

Correct Answer: ( 3)

CAT HCF and LCM Preparation Tips

Some tips for the preparation for CAT HCF and LCM are mentioned below.

• Develop a clear idea on the topics.
• Revise the formulas by practicing daily.
• Do solve previous years question paper
• Must give a mock test to increase speed for the exam.
• Start from the basic questions like
  • Find the Highest Common Factor of 25, 35 and 45.
  • Find the Least Common Multiple of 36 and 44.

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