This set of Aptitude Questions and Answers (MCQs) focuses on “HCF and LCM”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.

1. The HCF and LCM of two numbers is 15 and 1560. If one of the numbers is 120, find the other.

a) 195

b) 215

c) 255

d) 165

View Answer

Explanation: We know that, product of two numbers = HCF * LCM.

Other number = \(\frac{15*1560}{120}\)=195.

2. The sum and difference of LCM and HCF is 3175 and 3125 respectively. If the sum of the numbers is 575. Find the numbers.

a) 375 and 200

b) 225 and 350

c) 325 and 250

d) 400 and 175

View Answer

Explanation: Let the two numbers be x & y and their HCF & LCM be H & L respectively.

L + H = 3175 …… (i)

L – H = 3125 …… (ii)

Solving (i) and (ii), we get, L = 3150 and H = 25.

Given, x + y = 575.

We know that, product of two numbers = HCF * LCM.

x*y = H*L

x*(575-x) = 25*3150

x = 225 or 350.

If x = 225, then y = 350.

If x = 350, then y = 225.

Therefore, the numbers are 225 and 350.

3. The HCF and LCM of two numbers are 33 and 4719 respectively. When the first number is divided by 3, the quotient is 121, find the other number.

a) 469

b) 389

c) 359

d) 429

View Answer

Explanation: The first number is 121*3 = 363.

We know that, product of two numbers = HCF * LCM.

Other number = \(\frac{33*4719}{363}\)=429.

4. If the LCM of three numbers is 5896, then which of the following can be its HCF?

a) 13

b) 14

c) 17

d) 11

View Answer

Explanation: We know that LCM is a multiple of HCF.

From the given options 5896 is a multiple of 11. Hence, 11 can be its HCF.

5. Two numbers both greater than 31, have HCF 31 and LCM 4743. Find the sum of the numbers.

a) 799

b) 806

c) 781

d) 827

View Answer

Explanation: Let the 2 numbers be 31a and 31b.

We know that, product of two numbers = HCF * LCM.

31a * 31b = 31 * 4743.

So, a*b = 153.

The co-prime pairs of 153 are (1, 153) and (9, 17).

Since both the numbers are greater than 31, (1, 153) cannot be considered.

Therefore, the numbers are 9*31=279 and 17*31=527 and their sum is 279+527 = 806.

6. The HCF of two numbers is 27. Which of the following cannot be its LCM?

a) 351

b) 1053

c) 189

d) 1715

View Answer

Explanation: We know that HCF is a factor of LCM.

27 is a factor of 351, 1053 and 189. Therefore, 1715 cannot be its LCM.

7. The HCF of two numbers is 29 and the other two factors of LCM are 12 and 13. Find the larger of the two numbers.

a) 359

b) 363

c) 348

d) 377

View Answer

Explanation: Given, the HCF of two numbers is 29 and the other two factors of LCM are 12 and 13.

Therefore, the numbers should be 29*12 and 29*13. The larger number is 29*13=377.

8. The HCF of two numbers, each having 3-digits is 19 and their LCM is 1197. Find the sum of the numbers.

a) 196

b) 288

c) 304

d) 274

View Answer

Explanation: Let the two numbers be 19a and 19b.

We know that, product of two numbers = HCF * LCM.

19a*19b = 19*1197.

So, ab = 63.

9. The sum and difference of two numbers is 128 and 64 respectively. Find the HCF.

a) 32

b) 46

c) 54

d) 64

View Answer

Explanation: Let the two numbers be x and y respectively.

x + y = 128 …… (i)

x – y = 64 …… (ii)

On solving (i) and (ii), we get, x = 96 and y = 32.

Therefore, HCF of 32 and 96 is 32.

10. LCM of two prime numbers m and n (m>n) is 203. Then what is the value of 4y-x?

a) 0

b) -1

c) 1

d) -3

View Answer

Explanation: HCF of two prime numbers is 1.

Product of two numbers = 1*203 = 203.

Given m and n are the two numbers, such that mn = 203.

Co-prime pairs of 203 are (1, 203) and (29, 7).

Since, m and n are prime numbers, (1, 203) cannot be considered as 1 is neither prime nor composite.

Therefore m=29 and n=7.

4y-x = 4*7 – 29 = 28 – 29 = -1.

**More Aptitude Questions and Answers on HCF and LCM:**

- HCF and LCM Questions (Set 2)
- HCF and LCM Questions (Set 3)
- HCF and LCM Questions (Set 4)
- HCF and LCM Questions (Set 5)

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.