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LCM AND HCF TCS Questions: Asked in SSC MTS 2019 For 2021

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In this article, we provide LCM and HCF questions with their solutions asked by TCS in SSC MTS exams 2019 of MTS. These questions are useful for upcoming exams of SSC, Railways, and other competitive exams conducted by TCS.

SSC CGL Tier 2 2019 SSC CGL Tier 1 2019 SSC CHSL 2019 SSC CPO 2020 SSC MTS 2019
SSC CGL Tier 2 2018 SSC CGL Tier 1 2018 SSC CHSL 2018 SSC CPO 2019 SSC MTS 2017

SSC LCM and HCF Maths Questions 

Q1. The product of two numbers is 6845, if the HCF of the number is 37, then the greater number is:

दो संख्याओं का गुणनफल 6845 है | यदि संख्याओं का H.C.F 37 है, तो बड़ी संख्या ज्ञात करें |

SSC MTS 9 August 2019 (Morning)

(a). 111

(b). 37         

(c). 148

(d). 185

Q2. If y denotes HCF of x and y and x @ denotes LCM of x and y, then the value of (72×84) @ 144 is:  यदि x×y, x तथा y का महत्तम समापवर्तक है और  x @ y, x तथा y का लघुत्तम समापवर्त्य है, तो (72×84)@144 का मान होगा :

SSC MTS 9 August 2019 (Afternoon)

(a). 144

(b). 504          

(c). 210

(d). 420

Q3. The Highest Common Factor and Lowest Common Multiple of two numbers p and q are A and B respectively.  IF A+B = p+q, then the value of A3+B3 is : 

दो संख्याओं p तथा q का महत्तम समापवर्तक (HCF) एवं लघुत्तम समापवर्तक (LCM) क्रमसः A तथा B है, यदि A+B=p+q है, तो A3+B3का मान है:

SSC MTS  9 August 2019 (Evening)

(a) p3

(b) q3                 

(c) p3+q3

(d) p3-q3

Q4. If LCM of two numbers is 231, HCF of these two numbers is 11 and the first number is 77, then find the second number. यदि दो संख्याओं का लघुतम समापवर्तक 231 है, दोनों संख्याओं का महत्तम समापवर्तक 11 है तथा पहली संख्या 77 है, तो दूसरी संख्या है:

SSC MTS 13 August 2019 (Morning)

(a). 47

(b). 37         

(c). 57

(d). 33

Q5. What is the least number of square tiles required to pave the floor of a room 15m 17 cm long and 9 m 43 cm broad? 15 मी 17 सेमी लंबे तथा 9 मी 43 सेमी चौड़े कमरे की फर्श पर बिछाने के लिए आवश्यक वर्गाकार टाइलों की न्यूनतम संख्या ज्ञात करें |

SSC MTS 13 August 2019 (Evening)

(a). 851

(b). 841        

(c). 840

(d). 830

Q6. The Highest Common Factor and Lowest Common Factor of two numbers are 20 and 120. If one number is 50% more than the other number, then what is the smaller number? 

दो संख्याओं का महत्तम समापवर्तक और लघुतम समापवर्तक क्रमसः 20 और 120 है | यदि एक संख्या दूसरी संख्या से 50 % अधिक है, तो छोटी संख्या कौन सी है |

SSC MTS 14 August 2019 (Morning)

(a). 2

(b). 60    

(c). 40

(d). 80

Q7. If the LCM of two numbers 390 and 420 is 5460, then the HCF of two numbers is:

यदि दो संख्याओं 390 तथा 420 का लघुत्तम समापवर्त्य 5460 है, तो इन दोनों संख्याओं का महत्तम समापवर्तक क्या होगा?

SSC MTS 14 August 2019 (Evening)

(a). 35

(b). 45                 

(c). 30

(d). 42   

Q8. A temple has five bells which ring at intervals of 12, 15, 16, 20, and 25 minutes respectively. If they ring together at midnight, then at what time next will they ring together?

.एक मंदिर में 5 घंटियाँ हैं जो क्रमशः 12, 15, 16, 20 और 25 मिनट के अंतराल पर बजती हैं | यदि वे आधी रात में एक साथ बजती हैं, तो अगली बार वे किस समय एक साथ बजेंगी ? 

SSC MTS 16 August 2019 (Morning)

(a). 8:00 PM

(b). 7:00 PM          

(c). 7:30 PM

(d). 8:30 PM

Q9. What is the HCF of 20, 250, and 120? 

20, 250 तथा 120 का महत्तम समापवर्तक (HCF) कितना है?

SSC MTS 19 August 2019 (Afternoon)

(a). 15

(b). 10        

(c). 25

(d). 20

Q10. What is the LCM of the HCF of 2/3, 3/4, and LCM of 5/6, 7/8

2/3, 3/4 के म. स. तथा 5/6, 7/8 के ल. स. का ल. स. क्या है?

SSC MTS  20 August 2019 (Evening)

(a) 1/2

(b) 35/2                  

(c) 1/12

(d) 35/12

Q11. If two numbers are in the ratio of 7: 11, and their HCF is 13 then find their LCM. 

यदि दो संख्याओं का अनुपात 7:11 है और उनका म. स. 13 है, तो उसका ल. स. है:

SSC MTS  21 August 2019 (Morning)

(a) 101

(b) 1001                

(c) 143

(d) 234

Q12. The H.C.F and L.C.M of two numbers are 37 and 444 respectively. If the first number is 111, then the other number will be : 

दो संख्याओं का महत्तम और लघुतम समापवर्तक क्रमसः 37 और 444 है | यदि पहली संख्या 111 है तो दूसरी संख्या है:

SSC MTS  21 August 2019 (Afternoon)

(a) 333

(b) 74                

(c) 148

(d) 111

Q13. What is the smallest number which when increased by 5 is divisible by 12, 18 and 30?

वह सबसे छोटी संख्या कौन सी है जिसमें 5 की वृद्धि करने पर वह 12, 18 और 30 से विभाजित हो जाती है ? 

SSC MTS  2 August 2019 (Evening)

(a) 175

(b) 115             

(c) 235

(d) 195

Q14. What is the largest 4-digit number that is divisible by 32, 40, 36 and 48 ? 

4 अंकों की सबसे बड़ी संख्या कौन सी है, जो 32, 40, 36 तथा 48 से विभाज्य है?

SSC MTS  5 August 2019 (Evening)

(a) 9220

(b) 8820              

(c) 8640

(d) 9120

Q15. What is the largest two digit number which when divided by 6 and 7 gives remainder 3 and 4 respectively?

दो अंकों की वह सबसे बड़ी संख्या कौन सी है जिसे 6 और 7 से विभाजित करने पर शेष-फल क्रमशः 3 और 4 आता है | 

SSC MTS  8 August 2019 (Morning)

(a) 81

(b) 94             

(c) 83

(d) 84

Q16. If A is the smallest three digit number divisible by both 6 and 7 and B is the largest four digit number divisible by both 6 and 7, then what is the value of B-A?

यदि A , 6 और 7 दोनों से विभाजित होने वाली तीन अंकों की सबसे छोटी संख्या है तथा B , 6 और 7 दोनों से विभाजित होने वाली चार अंकों की सबसे बड़ी संख्या है, तो B-A का मान क्या होगा ? 

SSC MTS  8 August 2019 (Evening)

(a) 9912

(b) 9870                            

(c) 9996

(d) 9954

Q17. The largest three-digit number that is exactly divisible by 6, 7 and 8 is:

6,7 और 8 से विभाज्य तीन अंकों की सबसे बड़ी संख्या है : 

SSC MTS  13 August 2019 (Afternoon)

(a) 999

(b) 168                               

(c) 358

(d) 840

Q18. What is the highest number which when divides the numbers 1026, 2052 and 4102, leaves remainders 2, 4 and 6 respectively.

वह सबसे बड़ी संख्या कौन सी है जो संख्याओं 1026, 2052 और 4102 को विभाजित करने पर शेषफल क्रमशः 2, 4 और 6 छोड़ती है ? 

SSC MTS  14 August 2019 (Afternoon)

(a) 512

(b) 1024                           

(c) 128

(d) 256

Q19. Find the sum of digits of the largest 6-digit number that is divisible by 3, 4, 5 and 6. 

 3, 4, 5 और 6 द्वारा विभाजित होने वाली सबसे बड़ी 6-अंकीय संख्या के अंकों का योग कितना है?

SSC MTS  16 August 2019 (Afternoon)

(a) 45

(b) 39                                     

(c) 48

(d) 42

Q20. Let x be the smallest number greater than 600 which gives the remainders 2, 3 and 4, when divided by 5, 6 and 7 respectively. The sum of digits of x is:

मान लीजिये कि x,  600 से बड़ी सबसे छोटी संख्या है जो 5, 6 और 7 से विभाजित होने पर शेषफल क्रमशः 2, 3 और 4 छोड़ती है | x के अंकों का जोड़ है - 

SSC MTS  19 August 2019 (Evening)

(a) 14

(b) 15                                  

(c) 13

(d) 16

Q21. When the smallest number x is divided by 5,6,8,9 and 12, it gives remainder 1 in each case. But x is divisible by 13. What will be the remainder when x will be divided by 31 ? 

जब 5, 6, 8, 9 और 12 से सबसे छोटी संख्या x को विभाजित किया जाता है, तो प्रत्येक मामले में 1 शेष प्राप्त होता है, किन्तु x, 13 से विभाज्य है | जब x को 31 से विभाजित किया जाएगा तो प्राप्त शेष कितना होगा?

SSC MTS  20 August 2019 (Afternoon)

(a) 1

(b) 5                                    

(c) 3

(d) 0

Q22. Let x be the largest 4-digit number which when divided by 7, 8 and 11 leaves remainders 4, 5 and 8 respectively. When x is divided by (7+8+11), then the remainder will be :   

मान लिजिएं की x, 4 अंकों की सबसे बड़ी संख्या है, जिसे 7, 8 और 11 से विभाजित करने पर क्रमशः 4, 5 और 8 शेष बचता है | जब x को (7+8+11) से विभाजित किया जाता है, तब शेष होगा:

SSC MTS  21 August 2019 (Evening)

(a) 23

(b) 25                  

(c) 21

(d) 19

Q23. The difference between the two numbers is 15 and their HCF and LCM are 3 and 108 respectively. Find the difference between their inverses?

दो संख्याओं के बीच का अंतर 15 है और उनका महत्तम समापवर्तक (एच सी एफ) और लघुतम समापवर्तक (एल सी एम) क्रमश : 3 और 108 है | उनके व्युत्कर्मो के बीच अंतर ज्ञात कीजिए |

SSC MTS   16 August 2019 (Evening)

(a) 5/54

(b) 5/108              

(c) 5/81

(d) 5/112

Q24. What is the greatest number which can exactly divide 192, 1056 and 1584 ? 

वह सबसे बड़ी संख्या कौन सी है जो 192, 1056 तथा 1584 को पूर्णतः विभाजित कर सकती है ? 

SSC MTS 19 August 2019 (Morning)

(a) 48

(b) 56         

(c) 44

(d) 36

Q25. Let x and y be the 3-digit numbers such that their difference is 729 and HCF is 81. Find the value of (x+y) ?  / मान लीजिए एक x और y, 3-अंको की ऐसी संख्याएँ है कि उनका अंतर 729 और महत्तम समापवर्तक 81 है | (x+y) का मान ज्ञात कीजिए ?

SSC MTS 20 August 2019 (Morning)

(a) 1053

(b) 891                             

(c) 1539

(d) 1377

Here are the Solutions to the Above LCM and HCF Questions asked by TCS in MTS exams.

Sol 1.

Ans. (d)

Let the numbers are 37x and 37y

According to the question 

6845 = 37x x 37y

⇒ x×y = 5

Only possible factors of x and y are 1 and 5.

⇒ Greatest number = 37 x 5 = 185

Sol 2.

Ans. (a)

72 = 2x2x2x3x3

84 = 2x2x3x7

HCF of 72 and 84 = 2x2x3 = 12

Now, 

12 = 2x2x3

144 = 2x2x2x2x3x3

LCM of 12 and 144 =2x2x2x2x3x3 = 144

Sol 3. (c)

We know that

A3 +B3 =(A+B)(A2+B2-AB)

            = (A+B){(A+B)2-2AB-AB}

            = (A+B){(A+B)2-3AB}   ……..(1)

We know that ,

HCF × LCM = Number1 × Number2

⇒A×B = q

Put the values of AB and (A+B) in equation (1)

A3 +B3 = (p+q){(p+q)2-3pq}

          = (p+q)(p2+q2+2pq-3pq

          =  (p+q)(p2+q2-pq)

          =  p3 +q3

Sol 4. (d)

Let the required number = k

According to the question 

231 x 11 = 77 x k

⇒k = = 33

Sol 5.(a)

Length of the room = 1517 cm

Breadth of the room = 943 cm

HCF of 1517 and 943 = 41

Required number of tiles == 851

Sol 6.(c)

50% = 1/2

Let the smaller number = 2x and the bigger number = 3x

According to the question 

20 x 120 = 2x3x

x=20

So, the smaller number = 2 x 20 = 40

Sol 7. (c)

Let HCF of the numbers = h

According to the question 

5460 x h = 390 x 420

⇒ h=30

Sol 8. (a)

12 = 2x2x3

15 = 3x5

16 = 2x2x2x2

20 = 2x2x5

25 = 5x5

LCM of the numbers = 2x2x2x2x3x5x5 = 1200 minutes = 20 hours 

Required time = 12:00 AM + 20 hours = 8:00 PM

Sol 9.(b)

20 = 2x2x5

250 = 2x5x5x5 

120 = 2x2x2x3x5

Required HCF = 2x5 = 10

Sol 10. (b)

HCF of 2/3, 3/4 = HCF of 2 and 3 divided by LCM of 3 and 4.

HCF of 2 and 3 = 1

LCM of 3 and 4 = 12

HCF of 2/3, 3/4 = 1/12

LCM of 5/6, 7/8 = LCM of 5 and 7 divided by HCF of 6 and 8.

LCM of 5 and 7 = 35

HCF of 6 and 8 = 2

LCM of 5/6, 7/8 = 35/2

Now, 

LCM of 1/12, 35/2 = LCM of 1 and 35 divided by HCF of 12 and 2.

LCM of 1 and 35 = 35

HCF of 12 and 2 = 2

⇒LCM of 1/12, 35/2 = 35/2

 Sol 11.(b)

Ratio of two numbers = 7:11

HCF = 13

Required LCM = 7 x 11 x 13 = 1001

Sol 12. (c)

Let the second number = y

According to the question 

37 x 444 = 111 x y

⇒y=148

Sol 13. (a)

12 = 2x2x3

18 = 2x3x3

30 = 2x3x5

LCM of 12, 18 and 30 =2x2x3x3x5 = 180

Required number = 180-5 = 175

Sol 14. (c)

Largest number of four digits = 9999

32 = 2x2x2x2x2

40 = 2x2x2x5

36 = 2x2x3x3

48 = 2x2x2x2x3

LCM of 32, 40, 36 and 48 = 2x2x2x2x2x3x3x5 = 1440 

Required number = 9999-1359 = 8640

Sol 15. (a)

6-3 = 3 and 7-4 = 3

Largest number of two digit = 99

LCM of 6 and 7 = 6x7 = 42

Required number = 99-15-3 = 81

Sol 16. (b)

LCM of 6 and 7 = 7 x 6 = 42

Smallest number of three digits = 100

Smallest number of three digits divisible by 6 and 7 = A = 100 + (42-16) = 126

LCM of 6 and 7 = 7 x 6 = 42

Largest number of four digits = 9999

Largest number of four digits divisible by 6 and 7 = A = 9999-3 = 9996

Required difference = B-A = 9996-126 = 9870

Sol 17.(d)

Largest three digit number = 999

6 = 2x3

7 = 1x7

8 = 2x2x2

LCM of 6, 7 and 8 = 2x2x2x3x7 = 168

The largest three digit number divisible by 6,7 and 8 = 999-159 = 840

Sol 18. (b)

Let the required number = k

According to the question 

kx + 2 = 1026

⇒kx = 1024

ky + 4 = 2052

⇒ky = 2048

kz + 6 = 4102

⇒kz = 4096

So, k will be the HCF of 1024, 2048 and 4096

1024 = 210

2048 = 211

4096 = 212

⇒k = 210=1024

Sol 19. (d)

Biggest number of 6 digits = 999999

LCM of ,3,4,5,6 = 60

Required number = 999999-39 = 999960

Desired sum = 9+9+9+9+6+0 = 42

Sol 20. (b)

5-2 = 3, 6-3 = 3 and 7-4=3

LCM of 5, 6 and 7 = 210

Smallest number greater than 600 which is divisible by 5,6 and 7 = 210 x 3 = 630

Desired number = 630-3 = 627

Desired sum = 6+2+7 = 15

Sol 21. (b)

LCM of 5,6,8,9,12 = 360

⇒x = 360k+1

360k+1 will be divisible by 31 for the minimum value of  k = 10

Desired number = 3601

When 3601 is divided by 31 the remainder will be 5.

Sol 22.(b)

7-4 = 3, 8-5 = 3 and 11-8 = 3

Largest number of 4 digit = 9999

LCM of 7,8 and 11 = 616

Desired number = x = 9999-143-3 = 9853

Divisor = 7+8+11 = 26

Desired remainder = 985326= 25

Sol 23. (b) 

Let the numbers are 3k and 3m 

According to the question 

3k-3m = 15

⇒k-m=5or k = 5+m

And 

3 x 108 = 3k x 3m

⇒k.m=36

⇒m(5+m)=36

⇒5m+m2 -36=0

⇒m2+9m-4m-36=0

⇒m= 4 …….(m≠-9)

So, k=5+4 = 9

The two numbers will be 3(4) = 12 and 3(9) = 27

Desired difference = 1/12-1/27= 5/108

Sol 24. (a) 

192 = 2x2x2x2x2x2x3

1056 = 2x2x2x2x2x3x11

1584 = 2x2x2x2x3x3x11

Required HCF = 2x2x2x3 = 48

Sol 25. (a) 

According to the question 

x-y = 729

HCF= 81

Let the numbers be 81a and 81b.

Now, 81a - 81b = 729

⇒a - b = 9

Since, 81a < 1000

⇒ a < 12.34

a could be 10, 11 and 12

So, b could be 1, 2 and 3

If 81b > 100

⇒ b > 1.23

Hence, b could be 2 and 3.

and a could be 11 and 12.

Possible pairs of x and y = (891, 162) or (972, 243)

Since, HCF of (972, 243) = 243

Therefore, the required pair is (891, 162)

Hence, x + y = 891+162 = 1053

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