HCF and LCM Questions with Answers

HCF and LCM are important concepts in mathematics that help solve problems related to factors, multiples, and number relationships. This page covers both topics with solved examples, word problems, MCQs, and shortcuts to help students practise effectively.

What You'll Find on This Page

• 40+ HCF and LCM Questions
• Solved Examples
• Word Problems
• MCQs with Answers
• Questions on HCF and LCM of 3 Numbers
• Exam-Oriented Practice Sets
  
  

Table of Contents

• Key Terms
• Easy HCF and LCM Questions
• Medium HCF and LCM Questions
• Advanced HCF and LCM Questions
• Word Problems
• MCQ Questions
• HCF and LCM Practice Worksheet
• Tricks and Shortcuts
• 4 Mistakes to Avoid
• Conclusion
• Frequently Asked Questions On HCF and LCM Questions

 

Key Terms

Note: HCF is always less than or equal to the smaller number. LCM is always greater than or equal to the larger number.

Easy HCF and LCM Questions

Q1. Find the HCF of 18 and 45.

Answer:

18 = 2 × 3²

45 = 3² × 5

HCF = 3² = 9

Q2. Find the HCF of 24 and 36.

Answer:

24 = 2³ × 3

36 = 2² × 3²

HCF = 2² × 3 = 12

Q3. Find the LCM of 12 and 18.

Answer:

12 = 2² × 3

18 = 2 × 3²

LCM = 2² × 3² = 36

Q4. Find the LCM of 15 and 20.

Answer:

15 = 3 × 5

20 = 2² × 5

LCM = 2² × 3 × 5 = 60

Q5. Find the smallest number divisible by both 14 and 21.

Answer:

LCM of 14 and 21

14 = 2 × 7

21 = 3 × 7

LCM = 2 × 3 × 7 = 42

Practice Questions

1. Find the HCF of 20 and 30.

2. Find the HCF of 42 and 56.

3. Find the LCM of 8 and 12.

4. Find the LCM of 9 and 15.

5. Find the smallest number divisible by both 10 and 25.

Medium HCF and LCM Questions

Q1. Find the HCF of 48 and 72 using the division method.

Answer:

72 ÷ 48 = 1 remainder 24

48 ÷ 24 = 2 remainder 0

HCF = 24

Q2. Find the LCM of 8, 12 and 15.

Answer:

8 = 2³

12 = 2² × 3

15 = 3 × 5

LCM = 2³ × 3 × 5 = 120

Q3. The HCF of two numbers is 12 and their LCM is 180. One number is 60. Find the other number.

Answer:

HCF × LCM = Product of Numbers

12 × 180 = 60 × Other Number

Other Number = 36

Q4. LCM of two numbers is 120 and their HCF is 6. One number is 24. Find the other number.

Answer:

6 × 120 = 24 × Other Number

Other Number = 30

Q5. Find both the HCF and LCM of 24, 36 and 48.

Answer:

HCF = 12

LCM = 144

Practice Questions

1. Find the HCF of 56 and 84 using prime factorisation.

2. Find the LCM of 6, 8 and 12.

3. Find the HCF of 30, 45 and 60.

4. Find the LCM of 8, 12 and 18.

5. Find both HCF and LCM of 15, 25 and 35.

Read more:

• LCM questions
• HCF questions
• HCF and LCM

Advanced HCF and LCM Questions

Q1. The HCF of two numbers is 18 and their LCM is 540. If one number is 90, find the other number.

Answer:

HCF × LCM = Product of two numbers

18 × 540 = 90 × Other Number

Other Number = 9720 ÷ 90 = 108

Q2. Find the least number which when divided by 12, 18 and 24 leaves a remainder of 5 in each case.

Answer:

Required number = LCM(12, 18, 24) + 5

12 = 2² × 3

18 = 2 × 3²

24 = 2³ × 3

LCM = 2³ × 3² = 72

Required number = 72 + 5 = 77

Q3. Find the greatest number that divides 105, 165 and 255 leaving the same remainder in each case.

Answer:

Find HCF of:

165 − 105 = 60

255 − 165 = 90

HCF(60, 90) = 30

Q4. Three bells ring at intervals of 24 minutes, 36 minutes and 54 minutes. They ring together at 9:00 AM. When will they ring together again?

Answer:

LCM(24, 36, 54)

24 = 2³ × 3

36 = 2² × 3²

54 = 2 × 3³

LCM = 2³ × 3³ = 216

216 minutes = 3 hours 36 minutes

They will ring together again at 12:36 PM.

Q5. Find the HCF and LCM of 72, 108 and 180.

Answer:

72 = 2³ × 3²

108 = 2² × 3³

180 = 2² × 3² × 5

HCF = 2² × 3² = 36

LCM = 2³ × 3³ × 5 = 1080

Advanced Practice Questions

1. The HCF of two numbers is 24 and their LCM is 1440. If one number is 240, find the other number.

2. Find the least number that leaves remainder 7 when divided by 15, 20 and 25.

3. Find the greatest number that divides 180, 250 and 325 leaving the same remainder in each case.

4. Find the HCF and LCM of 84, 126 and 210.

5. Three traffic lights blink every 20 seconds, 30 seconds and 45 seconds. If they blink together now, after how many seconds will they blink together again?

HCF or LCM - how to decide

• Use HCF when the question asks to DIVIDE or SPLIT things into equal groups - "greatest number of students per row", "largest tile size", "maximum packets".
• Use LCM when the question asks about REPEATING events or finding the MINIMUM common value - "when will they meet again", "smallest number divisible by both", "after how many days".

Word Problems

Q1. Two bells ring at intervals of 12 minutes and 18 minutes. They ring together at 8:00 AM. When will they ring together again?

Answer: "When will they ring together" - two events repeating, asking when they coincide. That is LCM.

12 = 2² x 3

18 = 2 x 3²

LCM = 2² x 3² = 4 x 9 = 36 minutes

They will ring together again at 8:36 AM.

Q2. A teacher wants to arrange 48 boys and 60 girls in equal rows with no student left over. What is the maximum number of students in each row?

Answer: Splitting into equal groups, finding the maximum - HCF.

48 = 2⁴ x 3

60 = 2² x 3 x 5

HCF = 2² x 3 = 12

Maximum 12 students per row.

Q3. Three runners complete one lap in 30, 40 and 60 minutes respectively. They start together. After how many minutes will all three be at the starting point together again?

Answer: Three things repeating, asking when they all coincide. LCM of three numbers.

30 = 2 x 3 x 5

40 = 2³ x 5

60 = 2² x 3 x 5

LCM = 2³ x 3 x 5 = 8 x 3 x 5 = 120 minutes

Practice Questions

1. Find the largest number that divides 70, 105 and 175 exactly.
2. Two buses leave a station every 15 and 20 minutes. They leave together at 9:00 AM. When will they leave together again?
3. What is the smallest number of tiles (all the same size) that can exactly cover a floor of 6m x 9m without cutting any tile?

MCQ Questions

Tricks and Shortcuts

Frequently Asked Questions On HCF and LCM Questions

1. How to know the HCF and LCM?

Answer: To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers:

• HCF Method:

• List the factors of both numbers and find the greatest one common to both

• Or use the Euclidean algorithm (divide and take remainders)

• LCM Method:

• List multiples of both numbers and find the smallest one common to both

• Or use the formula:
  LCM(a, b) = (a × b) / HCF(a, b)

2. How do you know whether to use HCF or LCM?

Answer: Use HCF for dividing or grouping. And, use LCM for repeating events and common multiples.

3. What is the HCF of 24 and 36?

Answer: 

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

• HCF = 12

4. What are the LCM and HCF?

Answer: 

• LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers

• HCF (Highest Common Factor): The greatest number that divides two or more numbers exactly

5. What is the HCF of 645 and 473?

 Answer: Using the Euclidean algorithm:

• 645 ÷ 473 = 1 remainder 172

• 473 ÷ 172 = 2 remainder 129

• 172 ÷ 129 = 1 remainder 43

• 129 ÷ 43 = 3 remainder 0

HCF = 43

Keep practicing HCF and LCM problems to master the concept. Explore more math lessons and solved examples with Orchids The International School to strengthen your foundation!