# RRB NTPC LCM & HCF Questions PDF

Download RRB NTPC LCM & HCF Questions and Answers PDF. Top 25 RRB NTPC Maths questions based on asked questions in previous exam papers very important for the Railway NTPC exam.

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**Question 1: **If the LCM and HCF of two numbers are 72 and 12 respectively. Find the second number if one number is 36 ?

a) 24

b) 48

c) 12

d) 60

**Question 2: **Find the HCF of two numbers if LCM and product of those two numbers are 45 and 675 respectively ?

a) 25

b) 20

c) 15

d) 35

**Question 3: **Find the LCM and HCF of 196 and 392 ?

a) 196 & 392

b) 392 & 196

c) 392 & 14

d) 14 & 392

**Question 4: **Find LCM of 2/3 , 3/6, 4/12 ?

a) 4

b) 2

c) 3

d) 6

**Question 5: **Two numbers have their HCF as 9 and they are in the ratio 3:4 find their LCM ?

a) 72

b) 36

c) 108

d) 90

**Question 6: **Find the LCM of 7/2, 9/4 and 5/3 ?

a) 252

b) 21

c) 126

d) 315

**Question 7: **What is the difference between the LCM and HCF of 24, 48 ?

a) 12

b) 23

c) 54

d) 24

**Question 8: **Find the HCF of two numbers whose LCM is 38 and product of those two numbers is 266 ?

a) 4

b) 5

c) 6

d) 7

**Question 9: **Find LCM of two numbers, whose product is 864 and HCF is 12 ?

a) 72

b) 60

c) 36

d) 24

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**Question 10: **Find the HCF of 12, 24, 36, 30 ?

a) 18

b) 12

c) 6

d) 24

**Question 11: **Find the product of LCM and HCF of 48 and 72 ?

a) 432

b) 864

c) 1728

d) 3456

**Question 12: **Find the HCF of 3/2, 4/3, 5/4 ?

a) 1/12

b) 12

c) 1/6

d) 6

**Question 13: **If $x$ is a prime number, what is the LCM of $x^{18}, x^{24}$ and $x^{36}$

a) $x^{72}$

b) $x^{36}$

c) $x^{48}$

d) $x^{96}$

**Question 14: **Find the least common multiple of the numbers 36, 72 and 108.

a) 216

b) 108

c) 186

d) None of the above

**Question 15: **The HCF and LCM of two numbers are 3 and 150. If the sum of the numbers is 81, what is the sum of the reciprocals of the numbers?

a) 2/25

b) 9/50

c) 3/25

d) 7/150

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**Question 16: **The LCM of two numbers is 105. The numbers are in the ratio 7:5. What is the sum of the two numbers?

a) 36

b) 21

c) 15

d) 45

**Question 17: **What is the HCF of the fractions: ½, 5/7, 8/11, ¾ ?

a) 2/121

b) 1/154

c) 1/121

d) 1/308

**Question 18: **The least number n, where n>4, which when divided by 9, 11 and 12 leaves a remainder 4 is

a) 396

b) 400

c) 796

d) None of the above

**Question 19: **The product of HCF and LCM of two numbers is 525. If one of the numbers is 21, what is the other number?

a) 25

b) 30

c) 20

d) Cannot be determined

**Question 20: **Three numbers are in the ratio 1 : 2 : 5. Their LCM is 1600. What is the HCF of the three numbers?

a) 400

b) 800

c) 320

d) 160

**Question 21: **The greatest 3 digit number that is divisible by 20, 30, 50 and 60 is

a) 990

b) 900

c) 800

d) 750

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**Question 22: **The HCF of two numbers is 13 and the other two factors of their LCM are 5 and 9. What is the larger of the two numbers?

a) 45

b) 65

c) 117

d) 585

**Question 23: **HCF and LCM of two numbers are 11 and 825 respectively. If one number is 275 find the other number.

a) 53

b) 45

c) 33

d) 43

**Question 24: **Product of two coprime numbers is 117. Then their LCM is

a) 9

b) 13

c) 39

d) 117

**Question 25: **Two numbers are in the ratio 3:4. Their L.C.M. is 84. The greater number is

a) 21

b) 24

c) 28

d) 84

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**Answers & Solutions:**

**1) Answer (A)**

Let x be the second number,

LCM*HCF = Product of two numbers

72*12 = 36*x

x = 24

So the answer is option A.

**2) Answer (C)**

LCM*HCF = 675

(45)*HCF = 675

HCF = 675/45 = 15

So the answer is option C.

**3) Answer (B)**

Here 392 = 2*196, Hence LCM is 392 and HCF is 196

So the answer is option B.

**4) Answer (B)**

2/3 , 3/6, 4/12 = 2/3 , 1/2 , 1/3

LCM of fractions = (LCM of numerators)/(HCF of denominators) = (LCM of 2, 1, 1)/(HCF of 3,2,3) = 2/1 = 2

So the answer is option B.

**5) Answer (C)**

Two numbers have their HCF as 9 and they are in the ratio 3:4

Those numbers are 3*9=27 and 4*9=36

LCM of 27 and 36 is 108.

So the answer is option C.

**6) Answer (D)**

LCM of fractions = LCM of numerators/HCF of denominators

LCM of 7/2, 9/4 and 5/3 = (LCM of 7,9,5)/(HCF of 2,4,3) = 315/1 = 315

So the answer is option A.

**7) Answer (D)**

LCM of 24 and 48 = 48

HCF of 24 and 48 = 24

Difference = 24

So the answer is option D.

**8) Answer (D)**

LCM*HCF = product of two numbers

(38)*HCF = 266

HCF = 7

So the answer is option D.

**9) Answer (A)**

LCM*HCF = Product of numbers

LCM*12 = 864

LCM = 72

So the answer is option A.

**10) Answer (C)**

12 = 2*2*3

24 = 2*2*2*3

36 = 2*2*3*3

30 = 2*3*5

HCF = product of common factors = 2*3 = 6

So the answer is option C.

**11) Answer (D)**

Product of LCM & HCF of two numbers = product of those two numbers = 48*72 = 3456

So the answer is option D.

**12) Answer (A)**

HCF of fractions = (HCF of numerators)/(LCM of denominators) = (HCF of 3,4,5)/(LCM of 2,3,4) = 1/12

So the answer is option A.

**13) Answer (B)**

It is important to note that $x{36} = x^{24} \times x^{12}$.

Therefore, $x^{36}$ divides $x^{24}$

Similarly, $x^{36}$ divides $x^{18}$

Hence, $x^{36}$ divides both $x^{24}$ and $x^{18}$

Therefore, the LCM of $x^{18}, x^{24}$ and $x^{36}$ is $x^{36}$

**14) Answer (A)**

$36 = 2^2 * 3^2$

$72 = 2^3 * 3^2$

$108 = 2^2 * 3^3$

So, the LCM of the three numbers is $2^3 * 3^3$ = 8 * 27 = 216

**15) Answer (B)**

Let the numbers be x and 81-x.

LCM * HCF = 450 = x*(81-x)

=> $x^2 – 81x + 450 = 0$

So, x = 6 or 75

So, the sum of the reciprocals of the two numbers is 1/6 + 1/75 = (25+2)/150 = 27/150 = 9/50

**16) Answer (A)**

Let the two numbers be 7k and 5k.

LCM of 7 and 5 is 35. So, the LCM of the two numbers is 35k.

35k = 105 => k = 3

So, the two numbers are 7*3 = 21 and 5*3 = 15

The sum of the two numbers is 21+15 = 36

**17) Answer (D)**

The HCF of fractions is equal to HCF of numerators/LCM of denominators.

HCF of numerators = HCF of 1, 5, 8 and 3 = 1

LCM of numerators = LCM of 2, 7, 11 and 4 = 7*11*4 = 308

So, the HCF of the fractions is 1/308

**18) Answer (B)**

$9 = 3^2$

$12 = 3 * 2^2$

So, the LCM of 9, 11 and 12 is $3^2 * 2^2 * 11$ = 9 * 4 * 11 = 396

So, the required number should be of the form 396k + 4

For k = 1, the number becomes 396 + 4 = 400

**19) Answer (A)**

From the properties of LCM and HCF, we have:

Product of the two numbers = Product of HCF and LCM

21 * x = 525

So, the other number is 525/21 = 25

**20) Answer (D)**

Let the numbers be k, 2k and 5k. The LCM of 1, 2 and 5 is 10. So, the LCM of k, 2k and 5k is 10k.

10k = 1600 => k = 160

So, the three numbers are 160, 320 and 800. The HCF of the three numbers is 160.

**21) Answer (B)**

The LCM of 20, 30 and 60 is 60.

The LCM of 50 and 60 is 300.

So, the number should be of the form 300k.

For k = 3, the number is 300*3 = 900. For k > 3, the number will not be a 3-digit number. So, 900 is the answer.

**22) Answer (C)**

Let the two numbers be a*h and b*h, where ‘h’ is the HCF of the two numbers. The LCM of the two numbers is a*b*h.

Since the other two factors of the LCM are 5 and 9, the two numbers are 5*13 = 65 and 9*13 = 117

So, the larger of the two numbers is 117

**23) Answer (C)**

Let the number = $x$

HCF = 11 and LCM = 825

Product of HCF and LCM = Product of the two numbers

=> $x \times 275 = 11 \times 825$

=> $x = \frac{11 \times 825}{275}$

=> $x = \frac{825}{25} = 33$

=> Ans – (C)

**24) Answer (D)**

Let the two numbers be a,b.

Hence a * b = L.C.M(a,b) * G.C.D(a,b)

It is given that a,b are co-primes, implies G.C.D(a,b) = 1

Hence from the above equation we get L.C.M(a,b) = a*b = 117

**25) Answer (C)**

Let the numbers be 3x, 4x

LCM of 3x and 4x is = 12x

So the number 84 is divisible by 12

$\frac{84}{12}$ = 7

The numbers are 7×3 = 21 , 7x 4 = 28

The greatest number is 28

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