Previous Year HCF and LCM Questions for SSC CGL and CPO

     SSC CPO 2018

    1. The product of HCF and LCM of two numbers is 3321. If one of the numbers is 369, the HCF of the numbers is: 

    1. 21 
    2. 3 
    3. 9 
    4. 27

    2. The largest number of four digits that is exactly divisible by 15, 21 and 30 is : 

    1. 9840 
    2. 9910 
    3. 9830 
    4. 9870

    3. The greatest number of 5 digits that is exactly divisible by each of 8, 12, 15 and 20 is : 

    1. 99940 
    2. 99980 
    3. 99960 
    4. 99950

    4. Four bells ring simultaneously at a certain instant. Thereafter they ring at intervals of 6, 8, 10 and 12 seconds respectively. In how many minutes will they ring together again for the first time? 

    1. 1.5 min 
    2. 1 min 
    3. 2 min 
    4. 2.25 min

    5. The product of two numbers is 45360. If the HCF of the numbers is 36, then their LCM is :  

    1. 252 
    2. 630 
    3. 126 
    4. 1260

    6. The greatest number of four digits which is exactly divisible by 24, 36 and 54 is : 

    1. 9990 
    2. 9924 
    3. 9936 
    4. 9960

    7. The length, breadth and height of a box are 506 cm, 345 cm and 230 cm respectively. The length of the longest scale that will measure the three dimensions of the box is :  

    1. 46 cm 
    2. 23 cm 
    3. 15 cm 
    4. 30 cm

    8. The HCF and LCM of two numbers is 6 and 5040 respectively. If one of the numbers is 210, then the other number is: 

    1. 256 
    2. 144 
    3. 30 
    4. 630

    9. Which of the following of the statements is true? 

    1. LCM of two natural numbers is divisible by their HCF. 
    2. HCF+LCM of two numbers=Product of the two numbers. 
    3. Two prime numbers are co-prime numbers if their LCM is 1. 
    4. HCF of two numbers is the smallest common divisor of both numbers.

    10. What is the sum of digits of the least number, which when divided by 15, 18 and 42 leaves the same remainder 8 in each case and is also divisible by 13? 

    1. 25 
    2. 22 
    3. 24 
    4. 26

    11. Two numbers are in the ratio 6 : 11. If their HCF is 28, then the sum of these two numbers is: 

    1. 420 
    2. 392 
    3. 448 
    4. 476

    12. What is the sum of digits of the least number, which when divided by 15, 15 and 27 leaves the same remainder 9 in each case and is also divisible by 11? 

    1. 20 
    2. 17 
    3. 18 
    4. 19

    13. What is the sum of the digits of the least number, which when divided by 12, 16 and 54, leaves the same remainder 7 in each case, and is also completely divisible by 13? 

    1. 36 
    2. 16 
    3. 9 
    4. 27

    14. What is the sum of digits of the least number, which when divided by 15, 18 and 24 leaves the remainder 8 in each case and is also divisible by 13? 

    1. 16 
    2. 18 
    3. 17 
    4. 15

    SSC CPO 2019

    15. What is the HCF of 4/5 , 6/8, 8/25 ? 

    1. 1/200
    2. 1/100
    3. 1/5
    4. 1/50

    16. Which is the largest six-digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively? 

    1. 999982 
    2. 999956 
    3. 999960 
    4. 999964

    17. When 2388, 4309 and 8151 are divided by a certain 3-digit number, the remainder in each case is the same. The remainder is: 

    1. 15 
    2. 19 
    3. 39 
    4. 23

    18. Let x be the least 4-digit number which when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2800 and 3000, then what is the sum of the digits of x? 

    1. 16 
    2. 13 
    3. 12 
    4. 15

    19. If r is the remainder when each of 4749, 5601 and 7092 is divided by the greatest possible number d(>1), then the value of (d+r) will be: 

    1. 276 
    2. 271 
    3. 298 
    4. 282

    20. Let x be the least number of 4 digit that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2000 and2500, then what is the sum of the digits of x? 

    1. 9 
    2. 15 
    3. 10 
    4. 4

    21. In finding the HCF of two numbers by division method, the quotients are 1, 8 and 2 respectively, and the last divisor is 105. What is the sum of the numbers?  

    1. 3885 
    2. 3780 
    3. 3570 
    4. 3675

    22. Let x be the least number divisible by 16,24, 30, 36 and 45 and x is also a perfect square. What is the remainder when x is divisible by 123? 

    1. 103 
    2. 33 
    3. 100 
    4. 40

    23. When 3738, 5659 and 9501 are divided by the greatest possible number x, the remainder in each case is y. What is the sum of x and y? 

    1. 3738 
    2. 3783 
    3. 3673 
    4. 3637

    24. Let x be the least number divisible by 13, such that when x is divided by 4, 5, 6, 7, 8 and 12, the remainder in each case is 2. The sum of the digits of x is : 

    1. 11 
    2. 8 
    3. 9 
    4. 10

    25. What will be the sum of the biggest 3-digit number and smallest 4-digit number whose HCF is 23? 

    1. 1998 
    2. 1984 
    3. 2002 
    4. 2001

    26. HCF and LCM of two numbers is 8 and 48 respectively. If the ratio of two numbers is 2:3, then the larger of the two numbers is? 

    1. 16 
    2. 48 
    3. 18 
    4. 24

    27. The LCM of 165, 176, 385 and 495 is k. When k is divided by the HCF of the numbers, the quotient is p. What is the value of p? 

    1. 2520 
    2. 5040 
    3. 6720 
    4. 3360

    28. If r is the remainder when each of 6454, 7306 and 8797 is divided by the greatest number d (d > 1), then (d - r) is equal to : 

    1. 126 
    2. 64 
    3. 137 
    4. 149

    29. Let x be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but x is divisible by 11. The sum of digits of x is ... 

    1. 5 
    2. 6 
    3. 9 
    4. 4

    30. The sum of two numbers is 1215 and their HCF is 81. If the numbers lie between 500 and 700, then the sum of the reciprocals of the numbers is .. 

    1. 5/702
    2. 5/378
    3. 5/1512
    4. 5/1188

    SSC CPO 2020

    31. The ratio of two numbers is 7:11. If their highest common factor (HCF) is 28, find the difference between the two numbers. 

    1. 112 
    2. 28 
    3. 196 
    4. 308

    32. Find the smallest number that is divisible by 15, 18 and 36 to get 9 remainder in each case, and is divisible by 11. 

    1. 1089 
    2. 1080 
    3. 1071 
    4. 1269

    33. Find the smallest number which is completely divisible by 5, 6, 8, 10 and 12. 

    1. 180 
    2. 120 
    3. 240 
    4. 150

    34. The ratio of two numbers is 7:13 and their HCF is 8. Their (LCM): 

    1. 782 
    2. 728 
    3. 628 
    4. 872

    35. Find the smallest number which is completely divisible by 4, 5, 8 10 and 12? 

    1. 150 
    2. 180 
    3. 120 
    4. 240

    36. The HCF of two numbers is 29, and the other two factors of their LCM are 15 and 13. Find the larger number in those two numbers. 

    1. 435 
    2. 464 
    3. 406 
    4. 377

    37. When a number is divided by 3, 4 and 7, respectively, one gets 2, 3 and 5 remainder respectively. When the same number is divided by 84, find the remainder obtained. 

    1. 71 
    2. 53 
    3. 48 
    4. 30

    38. The ratio of two numbers is 7: 11. If their maximum common factor (HCF) is 28, then sum both numbers.

    1. 308 
    2. 196 
    3. 112 
    4. 504

    39. Find the sum of digits of smallest number that is divisible by 15, 18 and 36 to get 9 remainder in each case, and is divisible by 11.

    1. 17 
    2. 16 
    3. 18 
    4. 15

    40. When a number is divided by 3, 4 and 7 respectively, the remainder are obtained 2, 3 and 5 respectively. When the same number is divided by 42, find the remainder? 

    1. 30 
    2. 31 
    3. 29 
    4. 41

    41. The five bells ring together at intervals of 3, 5, 8, 9 and 10 seconds. All the bells ring together at the same time. After how long will they ring back together? 

    1. 8 min 
    2. 9 min 
    3. 6 min 
    4. 4 min

    42. Two numbers (HCF) are 29, and the other two factors of their (LCM) are 15 and 13. Find the smaller number in those two numbers. 

    1. 464 
    2. 377 
    3. 406 
    4. 435

    SSC CGL 2017 PRE

    43. What least value which should be added to 1812 to make it divisible by 7, 11 and 14? 

    1. 12 
    2. 36 
    3. 72 
    4. 154

    44. What is the HCF of 6345 and 2160? 

    1. 45 
    2. 135 
    3. 270 
    4. 15

    45. What is the LCM of 120 and 450? 

    1. 2400 
    2. 1800 
    3. 3600 
    4. 4800

    46. N is the largest three digit number which when divided by 6 and 5 leaves remainder 5 and 3 respectively. What will be the remainder when M is divided by 11? 

    1. 1 
    2. 2 
    3. 3 
    4. 4

    SSC CGL 2017 MAINS

    47. M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9? 

    1. 2 
    2. 3 
    3. 1 
    4. 6

    48. If the least common multiple of two numbers, 1728 and K is 1584, then how many values of K are possible? 

    1. 11 
    2. 8 
    3. 6 
    4. 7

    SSC CGL 2018

    49.  The LCM of two numbers x and y is 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x+y?  

    1. 660 
    2. 426 
    3. 852 
    4. 348

    50. In finding the HCF of two numbers by division method, the last divisor is 17 and the quotients are 1, 11 and 2, respectively. What is sum of the two numbers? 

    1. 833 
    2. 867 
    3. 816 
    4. 901

    51. Let x be the least number which when divided by 15, 18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square? 

    1. 39 
    2. 37 
    3. 43 
    4. 36

    52. The HCF of two numbers is 21 and their LCM is 221 times the HCF. If one of the numbers lies between 200 and 300, then the sum of the digits of the other number is? 

    1. 14 
    2. 17 
    3. 18 
    4. 15

    53. When 7897, 8110 and 8536 are divided by the greatest number x, then the remainder in each case is same. The sum of the digit of x is? 

    1. 14 
    2. 5 
    3. 9 
    4. 6

    54. When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 but x is divisible by 7. What is the digit at the thousands' place in x? 

    1. 5 
    2. 8 
    3. 4 
    4. 3 

    55. The sum of two positive numbers is 240 and their HCF is 15. Find the number of pairs of numbers satisfying the given conditions. 

    1. 8 
    2. 2 
    3. 5 
    4. 4

    56. Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when leaves no remainder.  

    1. 634 
    2. 366 
    3. 364 
    4. 384

    57. Let x be the greatest number which when divides 955 ,1027, 1075, the remainder in each case is the same. Which of the following is NOT a factor of x? 

    1. 6 
    2. 16 
    3. 4 
    4. 8

    58. When 1062, 1134 and 1182 are divided by the greatest number x , the remainder in each case is y. What is the value of (x-y)? 

    1. 17 
    2. 16 
    3. 19 
    4. 18


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