**LCM and HCF Questions for IBPS Clerk PDF:**

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**Question 1:Â **What least number would be subtracted from 427398 so that the remaining number is divisible by 15?

a)Â 13

b)Â 3

c)Â 16

d)Â 11

e)Â None of these

**Question 2:Â **Find the number which when multiplied by 13 is increased by 180:

a)Â 20

b)Â 15

c)Â 124

d)Â 5

e)Â None of these

**Question 3:Â **Find unit digit in $(515)^{31}$ + $(515)^{90}$

a)Â 0

b)Â 5

c)Â 1

d)Â 4

e)Â None of these

**Question 4:Â **What is the unit digit in (476 x 198 x 359 x 242)?

a)Â 8

b)Â 6

c)Â 4

d)Â 2

e)Â None of these

**Question 5:Â **Find the least value of k so that 39 k20 is divisible by 3

a)Â 1

b)Â 3

c)Â 5

d)Â 2

e)Â None of these

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**Question 6:Â **Find the least value of K so that 36 K36 is divisible by 6.

a)Â 1

b)Â 6

c)Â 2

d)Â 0

e)Â None of these

**Question 7:Â **Find the HCF of 1/2 and 3/2

a)Â 3/2

b)Â 1/2

c)Â 1

d)Â 3

e)Â None of these

**Question 8:Â **Find the number of divisors of 10800

a)Â 57

b)Â 60

c)Â 72

d)Â 62

e)Â None of these

**Question 9:Â **N = n! Where n is natural number. The unitâ€™s digit of N canâ€™t be

a)Â 2

b)Â 6

c)Â 5

d)Â 0

e)Â None of these

**Question 10:Â **Find the number of prime factors of $2^{11}\times7^5\times11^6$

a)Â 22

b)Â 21

c)Â 6

d)Â 18

e)Â None of these

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**Question 11:Â **Find the greatest number which will divide 321,428 and 535 exactly

a)Â 105

b)Â 107

c)Â 109

d)Â 102

e)Â None of these

**Question 12:Â **Which is smallest prime number?

a)Â 0

b)Â 1

c)Â 2

d)Â 3

e)Â None of these

**Question 13:Â **Which of the following is a prime number?

a)Â 149

b)Â 437

c)Â 319

d)Â 567

e)Â None of these

**Question 14:Â **Find the least number which is exactly divisible by 12, 15, 20 and 27.

a)Â 650

b)Â 520

c)Â 600

d)Â 540

e)Â None of these

**Question 15:Â **Find the sum of all natural-numbers between 100 and 175

a)Â 10450

b)Â 10175

c)Â 10170

d)Â 10435

e)Â None of these

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**Question 16:Â **What least number must be subtracted from 3475 to make it divisible by 50 ?

a)Â 75

b)Â 100

c)Â 25

d)Â 50

e)Â None of these

**Question 17:Â **How many numbers up to 800 are divisible by 24?

a)Â 30

b)Â 29

c)Â 33

d)Â 26

e)Â None of these

**Question 18:Â **How many numbers up to 700 are divisible by both 3 and 5?

a)Â 42

b)Â 46

c)Â 39

d)Â 52

e)Â None of these

**Question 19:Â **How many numbers less than 10,000 are there which are divisible by 21, 35 and 63?

a)Â 33

b)Â 32

c)Â 38

d)Â 31

e)Â None of these

**Question 20:Â **Find the number nearest to 2559 which is exactly divisible by 35

a)Â 2535

b)Â 2555

c)Â 2540

d)Â 2560

e)Â None of these

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**Answers & Solutions:**

**1)Â AnswerÂ (B)**

Apply the divisibility rules of 3 and 5. For a number to be divisible be divisible by 5, it should end with 0 or 5. So, subtracting 3 from the number makes it divisible by 5. It is also divisible by 3 then. So, it is divisible by 15.

**2)Â AnswerÂ (B)**

M-I: 13x = 180 +x

13x -x= 180 or 12x = 180

x= 15

M-II: OTP

**3)Â AnswerÂ (A)**

Since the unit digit of any number which is ending in 5 to the power of any number will be 5 only. Thus Units place of $(515)^{31}$ as well as $(515)^{90}$ is 5. Since the sum of Units place of total expression is 5 + 5 = 10, thus Zero is the unit’s place of the given expression.

**4)Â AnswerÂ (C)**

Unit digit in 476 x 198 x 359 x 242

= unit digit in 6 x 8 x 9 x 2 = 4

**5)Â AnswerÂ (A)**

3 + 9 + K + 2 + 0 = 14 + K

Least value of K is 1

**6)Â AnswerÂ (D)**

Given number is divisible by 6, if it is divisible by both 2 and 3.

âˆ´The least value of K is 0

**7)Â AnswerÂ (B)**

HCF of 1/2 , 3/2 = (HCF of 1 and 3)/(LCM of 2 and 2) = 1/2

**8)Â AnswerÂ (B)**

$10800 = 2^4 * 5^2 * 3^3$

Number of divisors = (4+1) (2+1) (3 + 1) = 60

**9)Â AnswerÂ (C)**

Since, n ! is always even for n > 1. Therefore, 5 cannot be the unit digit

**10)Â AnswerÂ (A)**

Number of prime factors

= 11 + 5 + 6 = 22

**11)Â AnswerÂ (B)**

Required number

= HCF of 321, 428 and 535 = 107

**12)Â AnswerÂ (C)**

2 is the smallest prime number

**13)Â AnswerÂ (A)**

We know that $13^2$ > 149

Prime numbers less than 14 are 2, 3, 5, 7, 11

Clearly none of the numbers divide 149

Therefore, 149 is a prime number.

**14)Â AnswerÂ (D)**

Required number = LCM of 12, 15, 20 and 27 = 540

**15)Â AnswerÂ (B)**

Between 100 and 175 means excluding 100 and 175.

Sum of natural numbers up to 100 (100Ã— 101)/2 = 5050

Sum of natural numbers up to 174 =(174Ã—175)/2=15225

âˆ´ required sum = 15225-5050 = 10175

**16)Â AnswerÂ (C)**

Remainder when 3475 is divided by 50 is 25.

âˆ´ Least number that should be subtracted =25

**17)Â AnswerÂ (C)**

Quotient when 800 is divided by 24 is 33.

There are 33 numbers up to 800 divisible by 24

**18)Â AnswerÂ (B)**

Quotient when 700 is divided by the LCM of 3 and 5 i.e., 15 is 46.

âˆ´There are 46 numbers up to 700

**19)Â AnswerÂ (D)**

LCM (21, 35, 63) = 315

The numbers less than 10,000 which are divisible by 315 are given by [10,000/315] i.e the integral part when 10,000 is divided by 315 is 31.

The required answer is 31

**20)Â AnswerÂ (B)**

The two numbers nearest to 2559 divisible by 35 are

a) 2559 – 4 = 2555

b) 2559 + (35 – 4 ) = 2590

âˆ´The required number is 2555.