# HCF and LCM Questions for SSC CGL And CHSL Pdf HCF and LCM Concept

Prime Number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
For example, 2, 3, 5, 7, 11, 13, etc. are prime numbers.

Co-Prime Number: Two numbers are said to be relatively prime, mutually prime, or co-prime to each other when they have no common factor or the only common positive factor of the two numbers is 1.
In other words, two numbers are said to be co-primes if their H.C.F. is 1.

Factors: The numbers are said to be factors of a given number when they exactly divide that number.
Thus, factors of 18 are 1, 2, 3, 6, 9 and 18.

Common Factors: A common factor of two or more numbers is a number which divides each of them exactly.
Thus, each of the numbers – 2, 4 and 8 is a common factor of 8 and 24.

Multiple: When a number is exactly divisible by another number, then the former number is called the multiple of the latter number.
Thus, 45 is a multiple of 1, 3, 5, 9, 15 and 45.

Common Multiple: A common multiple of two or more numbers is a number which is exactly divisible by each of them.
For example, 12, 24 and 36 is a common multiple of 3, 4, 6 and 12.

Prime Factorisation: If a natural number is expressed as the product of prime numbers, then the factorisation of the number is called its prime factorisation.
A prime factorisation of a natural number can be expressed in the exponential form.
For example:
(1) 24 = 2 x 2 x 2 x 3 = 23 x 3.
(2) 420 = 2 x 2 x 3 x 5 x 7 = 22 x 3 x 5 x 7

 Highest Common Factor (H.C.F.) or Greatest Common Divisor (G.C.D.) or Greatest Common Measure (G.C.M.) are synonymous terms: The H.C.F of two or more than two numbers is the greatest numbers which divides each of them without any remainder. Methods of finding the H.C.F. of a given set of numbers:

# HCF and LCM Questions

1. The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is (SSC CGL 1st Sit. 2010)

(a) 48
(b) 36
(c) 24
(d) 16
Ans. (d) 16

2. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is (SSC CGL 1st Sit. 2010)

(a) 1120
(b) 4714
(c) 5200
(d) 5600
Ans. (b) 4714

3. The ninth term of the sequence 0, 3, 8, 15, 24, 35,…. is (SSC CGL 1st Sit. 2010)

(a) 63
(b) 70
(c) 80
(d) 99
Ans. (c) 80

4. A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be (SSC CGL 1st Sit. 2010)

(a) 1
(b) 2
(c) 7
(d) 17
Ans. (b) 2

5. Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is (SSC CGL 1st Sit. 2010)

(a) 21
(b) 24
(c) 28
(d) 84
Ans. (c) 28

6. The sixth term of the sequence 2, 6, 11, 17, ….. is (SSC CGL 1st Sit. 2010)

(a) 24
(b) 30
(c) 32
(d) 36
Ans. (c) 32

7. A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, the remainder will be (SSC CGL 2nd Sit. 2010)

(a) 9
(b) 7
(c) 3
(d) 2
Ans. (d) 2

8. A 4–digit number is formed by repeating a 2–digit number such as 1515, 3737, etc. Any number of this form is exactly divisible by (SSC CGL 2nd Sit. 2010)

(a) 7
(b) 11
(c) 13
(d) 101
Ans. (d) 101

9. The H.C.F. and L.C.M. of two numbers are 12 and 336 respectively. If one of the numbers is 84, the other is (SSC CGL 2nd Sit. 2010)

(a) 36
(b) 48
(c) 72
(d) 96
Ans. (b) 48

10. The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is (SSC CGL 2nd Sit. 2010)

(a) 2/35
(b) 3/25
(c) 4/35
(d) 2/25
Ans. (c) 4/35

11. If ‘n’ be any natural number, then by which largest number (n3 – n) is always divisible? (SSC CGL 2nd Sit. 2010)

(a) 3
(b) 6
(c) 12
(d) 18
Ans. (b) 6

12. How many perfect squares lie between 120 and 300 ? (SSC CGL 2nd Sit. 2010)

(a) 5
(b) 6
(c) 7
(d) 8
Ans. (c) 7

13. The remainder when 321 is divided by 5 is (SSC CGL 1st Sit. 2011)

(a) 1
(b) 2
(c) 3
(d) 4
Ans. (c) 3

14. The last digit of (1001) 20008  +  1002 is (SSC CGL 1st Sit. 2011)

(a) 0
(b) 3
(b) 4
(d) 6
Ans. (b) 3

15. If x * y = (x + 3)2 (y –1), then the value of 5 * 4 is (SSC CGL 1st Sit. 2011)

(a) 192
(b) 182
(c) √2
(d) 356
Ans. (c) √2

16. The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F. ? (SSC CGL 1st Sit. 2011)

(a) 8
(b) 12
(c) 24
(d) 35
Ans. (d) 35

17. A number when divided by 49 leaves 32 as remainder. This number when divided by 7 will have the remainder as (SSC CGL 1st Sit. 2011)

(a) 4
(b) 3
(c) 2
(d) 5
Ans. (a) 4

18. The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10: 15 : 00 AM, then at what time will they again change simultaneously? (SSC CGL 1st Sit. 2011)

(a) 10 : 16 : 54 AM
(b) 10 : 18 : 36 AM
(c) 10 : 17 : 02 AM
(d) 10 : 22 : 12 AM
Ans. (b) 10 : 18 : 36 AM

19. The least number, which is to be added to the greatest number of 4 digits so that the sum may be divisible by 345, is (SSC CGL 2nd Sit. 2011)

(a) 50
(b) 6
(c) 60
(d) 5
Ans. (b) 6

20. If 17200 is divided by 18, the remainder is (SSC CGL 2nd Sit. 2011)

(a) 1
(b) 2
(c) 16
(d) 17
Ans. (a) 1

21. The unit digit in the sum of (124) 372 + (124)373 is (SSC CGL 2nd Sit. 2011)

(a) 5
(b) 4
(c) 2
(d) 0
Ans. (d) 0

22. If a * b = ab, then the value of 5 * 3 is (SSC CGL 2nd Sit. 2011)

(a) 125
(b) 243
(c) 53
(d) 15
Ans. (a) 125

23. Which one of the following will completely divide 571 + 572 + 573 ? (SSC CGL 2nd Sit. 2011)

(a) 150
(b) 160
(c) 155
(d) 30
Ans. (c) 155

24. L.C.M. of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers ? (SSC CGL 2nd Sit. 2011)

(a) 140
(b) 80
(c) 60
(d) 70
Ans. (d) 70

25. When ‘n’ is divisible by 5 the remainder is 2. What is the remainder when n2 is divided by 5? (SSC CGL 2nd Sit. 2011)

(a) 2
(b) 3
(c) 1
(d) 4
Ans. (d) 4

26. Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time they meet at the starting point for the first time? (SSC CGL 2nd Sit. 2011)

(a) 1800 seconds
(b) 3600 seconds
(c) 2400 seconds
(d) 4800 seconds
Ans. (a) 1800 seconds

27. The greatest number that can divide 140, 176, 264 leaving remainders of 4, 6, and 9 respectively is (SSC Sub. Ins. 2012)

(a) 85
(b) 34
(c) 17
(d) 2
Ans. (c) 17

28. There are 4 terms in an A.P. such that the sum of two means is 110 and product of their extremes is 2125. The 3rd term is (SSC Sub. Ins. 2012)\

(a) 65
(b) 75
(c) 55
(d) 45
Ans. (a) 65

29. The number nearest to 75070 which is divisible by 65, is (SSC CGL 1st Sit. 2012)
(a) 75070
(b) 75075
(c) 75010
(d) 75065
Ans. (b) 75075

30. The least number which when divided by 35, 45, 55 leaves the remainder 18, 28, 38 respectively is (SSC CGL 1st Sit. 2012)

(a) 3448
(b) 3482
(c) 2468
(d) 3265
Ans. (a) 3448

31. A three-digit number 4a3 is added to another three-digit number 984 to give the four digit number 13b7 which is divisible by 11. Then the value of (a + b) is : (SSC CGL 1st Sit. 2012)

(a) 11
(b) 12
(c) 9
(d) 10
Ans. (d) 10

32. The greatest number that will divide 19, 35 and 59 to leave the same remainder in each case is : (SSC CGL 1st Sit. 2012)

(a) 9
(b) 6
(c) 7
(d) 8
Ans. (d) 8

33. The next term of the series – 1, 6, 25, 62, 123, 214, _____ is : (SSC CGL 1st Sit. 2012)

(a) 345
(b) 143
(c) 341
(d) 343
Ans. (c) 341

34. The next term of the series 1, 5 12, 24, 43 is (SSC CGL 1st Sit. 2012)

(a) 51
(b) 62
(c) 71
(d) 78
Ans. (c) 71

35. The least multiple of 13 which when divided by 4, 5, 6, 7 leaves remainder 3 in each case is (SSC CGL 2nd Sit. 2012)

(a) 3780
(b) 3783
(c) 2520
(d) 2522
Ans. (b) 3783

36. What would be the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + ……. up to 15th term? (SSC CGL 2nd Sit. 2012)

(a) 250
(b) 240
(c) 225
(d) 265
Ans. (c) 225

37. The least number which when divided by 48, 64, 90, 120 will leave the remainders 38, 54, 80, 110 respectively, is (SSC CGL 2nd Sit. 2012)

(a) 2870
(b) 2860
(c) 2890
(d) 2880
Ans. (a) 2870

38. If 13 + 23 + ……. + 93 = 2025, then the approx. value of (0.11)3 + (0.22)3 + ……. + (0.99)3 is (SSC CGL 2nd Sit. 2012)

(a) 0.2695
(b) 0.3695
(c) 2.695
(d) 3.695
Ans. (c) 2.695

39. With a two digit prime number, if 18 is added, we get another prime number with digits reversed. How many such numbers are possible? (SSC CGL 2nd Sit. 2012)

(a) 2
(b) 3
(c) 0
(d) 1
Ans. (a) 2

40. If x = (√3 – √2)/(√3 – √2) + and y = (√3 + √2)/(√3 – √2), then the value of x 3+ y 3 is: (SSC Sub. Ins. 2013)

(a) 950
(b) 730
(c) 650
(d) 970
Ans. (d) 970

41. The ratio of two numbers is 3: 4 and their HCF is 5. Their LCM is : (SSC Sub. Ins. 2013)

(a) 10
(b) 60
(c) 15
(d) 12
Ans. (b) 60

42. L.C.M. of 2/3, 4/9, 5/6 is (SSC CHSL 2013)

(a) 20/27
(b) 8/27
(c) 20/3
(d) 10/3
Ans. (c) 20/3

43. ‘a’ divides 228 leaving a remainder 18. The biggest two-digit value of ‘a’ is (SSC CHSL 2013)

(a) 30
(b) 30
(c) 21
(d) 35
Ans. (b) 30

44. If the sum of the digits of any integer lying between 100 and 1000 is subtracted from the number, the result always is (SSC CHSL 2013)

(a) divisible by 5
(b) divisible by 6
(c) divisible by 2
(d) divisible by 9
Ans. (d) divisible by 9

45. The fifth term of the sequence for which t1 = 1, t2 = 2 and tn+2 = tn + t n+1, is (SSC CGL 1st Sit. 2013)

(a) 5
(b) 10
(c) 6
(d) 8
Ans. (d) 8

46. Product of two co-prime numbers is 117. Then their L.C.M. is (SSC CGL 2013)

(a) 13
(b) 39
(c) 117
(d) 9
Ans. (c) 117

47. A number x when divided by 289 leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is (SSC CGL 2nd Sit. 2013)

(a) 3
(b) 1
(c) 5
(d) 2
Ans. (b) 1

48. The sum of the squares of the digits of the largest prime number in two digits is (SSC Multitasking 2014)
(a) 148
(b) 130
(c) 97
(d) 118
Ans. (b) 130

49. Find the number lying between 900 and 1000 which when divided by 38 and 57 leaves in each case a remainder 23. (SSC Multitasking 2014)
(a) 912
(b) 926
(c) 935
(d) 962
Ans. (c) 935

50. The next term of the sequence,
(1 + 1/2), (1+1/2)(1+1/3),(1+1/2)(1+1/3)(1 + 1/4), __ is (SSC Sub. Ins. 2014)
(a) 3
(b) (1+1/5)
(c) 5
(d) (1+1/2)(1/1/5)
Ans. (a) 3

51. Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three container exact number of times is (SSC Sub. Ins. 2014)

(a) 31 litres
(b) 62 litres
(c) 41 litres
(d) 84 litres
Ans. (a) 31 litres

52. The H.C.F. and L.C.M. of two numbers are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is (SSC CHSL 2014)

(a) 147
(b) 528
(c) 132
(d) 264
Ans. (c) 132

53. A teacher wants to arrange his students in an equal number of rows and columns. If there are 1369 students, the number of students in the last row are (SSC CHSL 2014)

(a) 37
(b) 33
(c) 63
(d) 47
Ans. (a) 37

54. The first term of an Arithmetic Progression is 22 and the last term is –11. If the sum is 66, the number of terms in the sequence are : (SSC CHSL 2014)

(a) 10
(b) 12
(c) 9
(d) 8
Ans. (b) 12

55. If the product of first fifty positive consecutive integers be divisible by 7n, where n is an integer, then the largest possible value of n is (SSC CGL 1st Sit. 2014)

(a) 7
(b) 8
(c) 10
(d) 5
Ans. (b) 8

56. The smallest five digit number which is divisible by 12, 18 and 21 is : (SSC CHSL 2015)
(a) 50321
(b) 10224
(c) 30256
(d) 10080
Ans. (d) 10080

57. If 13 + 23 + ….. + 10 3 – 3025, then the value of 23 + 43 +….. + 203 is : (SSC CHSL 2015)
(a) 5060
(b) 12100
(c) 24200
(d) 7590
Ans. (c) 24200

58. The least number that should be added to 2055 so that the sum is exactly divisible by 27: (SSC CGL 1st Sit. 2015)
(a) 24
(b) 27
(c) 31
(d) 28
Ans. (a) 24

59. The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case is: (SSC CGL 2nd Sit. 2015)

(a) 178
(b) 182
(c) 176
(d) 180
Ans. (b) 182

60. What least value must be assigned to ‘*’ so that the numbers 451*603 is exactly divisible by 9? (SSC CGL 1st Sit. 2016)

(a) 7
(b) 8
(c) 5
(d) 9
Ans. (b) 8