HCF LCM Exercises

Abhishek Jain

1. Find the L.C.M. of 36, 48, 72 and 108. a.432 b. 428 c. 360 d. 106 e. None of these 2. The H.C.F and L.C.M. of any two numbers are 2079 and 27 respectively. If one of the two numbers is 189, find the other number. a. 309 b. 297 c. 180 d. 327 e. None of these 3. Find the greatest number that will divide 296, 492 and 1246 leaving remainders 8, 12 and 22 respectively a.12 b. 36 c. 24 d. 48 e. None of these 4. Which of following is a pair of co - prime number? a.32,52 b. 16,28 c. 18,35 d. 21,42 e. None of these 5. The L.C.M. of two numbers is 252 and their ratio is 6:7. Find the numbers. a. 32, 49 b. 16, 25 c. 36,42 d. 54,63 e. None of these 6. A room is 2.47m long and 2.09m broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for floor. a. 143 b. 361 c. 142 d. 165 e. None of these 7. Find the greatest number that will divide 378, 330 and 882 leaving remainders 3, 5 and 7 respectively.

a. 25 b. 220 c. 300 d. 275 e. None of these 8. Which smallest number must be added to 9373 so that it exactly divisible by 4? a. 3 b. 2 c. 1 d. 4 e. None of these 9. Which smallest number must be added to 605329 so that it becomes divisible by 9? a. 3 b. 2 c. 5 d. 7 e. None of these 10. Six bells tolling at the interval of 2, 4, 6, 8, 10, and 12 seconds respectively. In 30 minutes how many times they toll? a. 4 b. 10 c. 15 d. 16 e. None of these 11. Find the L.C.M. of 6/7, 12/13, 7/15. a. 84 b. 1/84 c. 13 d. 1/13 e. None of these 12. The sum and the differences of the L.C.M. and the H.C.F. of two numbers are 312 and 264, respectively. Find the bigger number if their sum is 168. a. 108 b. 92 c. 96 d. 100 e. None of these 13. Find the H.C.F. of 120, 140, 180 and 420. a. 15 b. 20 c. 25 d. 30 e. None of these 14. Find the least number which when divided by 36, 48 and 54 which will leaves the same remainder 7. a. 432 b. 436 c. 437 d. 439 e. None of these

15. Find the greatest number which on dividing 304, 554 and 854 leaves equal remainder. a. 35 b. 65 c. 50 d. 60 e. None of these 16. Find the greatest number which on dividing 277, 757 and 3307 leaves the same remainder 7 in each case. a. 30 b. 15 c. 60 d. 25 e. None of these 17. Find the L.C.M. of 9/10, 12/25, 18/35, 21/40. a. 5/252 b. 3/1400 c. 252/5 d. 1400/3 e. None of these 18. Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder. a. 6 b. 9 c. 8 d. 10 e. None of these 19. A wholesale sugar dealer has 780kilogram, 1650kilogram and 510kilogram sugar of three different qualities. He has to pack it all into boxes of equal size without mixing. Find the capacity of the largest possible box. a. 15 b. 30 c. 12 d. 25 e. None of these 20. Find the least perfect square number which is divisible by 2,3,4,5,6. a. 3600 b. 900 c. 1600 d. 2500 e. None of these 21. Six bells commence tolling together and toll at intervals of 2, 4, 7, 8, 10 and 12 seconds respectively. In 30 minutes how many times do they toll together? a. 2 b. 3 c. 4 d. 5 e. None of these

22. Seven bells ring at intervals of 2, 3, 4, 6, 8, 9 and 12 minutes, respectively. They started ringing simultaneously at 6.00 in the morning. How many more times would all seven bells ring simultaneously till 5.00 in the evening of the same day? a. 6 b. 7 c. 8 d. 9 e. None of these 23. Find the LCM of 5/2, 8/9, 11/14 a. 400 b. 420 c. 440 d. 460 e. None of these 24. Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case a. 35 b. 25 c. 45 d. 55 e. None of these 25. An electric wire is sold only in multiplier of 1 metre and a person required several lengths of wire, each 85 cm long. To avoid any wastage and to minimize labour, he should purchase minimum length of a. 17m b. 17cm c. 170cm d. 1.7m e. None of these 26. Find the greatest number that will divide 55, 127 and 175, so as to leave the same remainder in each case a. 12 b. 18 c. 24 d. 30 e. None of these 27. Find the largest number of four digits exactly divisible by 12, 15, 18 and 27 a. 9999 b. 9920 c. 9720 d. 9520 e. None of these 28. The circumferences of the fore and hind wheels of a carriage are respectively. At any given moment, a chalk

mark is put on the point of contact of each wheel with the ground. Find the distance travelled by the carriages so that both the chalk marks are again on the ground at the same time a. 217.5m b. 2175m c. 217.5cm d. 2175m e. None of these 29. Find the greatest number that will divide 478 and 719 leaving remainders 2 and 5 Respectively a. 236 b. 238 c. 240 d. 119 e. None of these 30. A certain card game has a special pack. If you deal out equally to five players there are two cards left undealt. The same is true if you deal to seven players. If the cards are dealt to three players there is one left undealt. Number of cards that cannot be there in the pack is a. 100 b. 150 c. 125 d. 175 e. None of these 31. The HCF of two numbers is 113 and their LCM is 228825. One of the numbers is 2825. Find the other a. 9153 b. 9150 c. 9163 d. 9125 e. None of these 32. Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. The numbers are a. 12 , 24 , 36 b. 1 , 2 , 3 c. 6 , 12 , 18 d. 24 , 48 , 72 e. None of these 33. The least number of five digits which is exactly divisible by 12, 15 and 18 is a. 10000 b. 10020 c. 10800 d. 10080 e. None of these

34. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? a. 10 b. 15 c. 16 d. 14 e. None of these 35. The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all chance simultaneously at 8: 20: 00 hours, then they will again change simultaneously at a. 8:27:12 hours b. 8:26:06 hours c. 8:25:12 hours d. 8:27:08 hours e. None of these 36. The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is a. 23 b. 46 c. 1 d. 92 e. None of these 37. The L.C.M of three different numbers is 120. Which of the following cannot be their H.C.F? a. 12 b. 24 c. 48 d. 8 e. Data inadequate 38. The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of such numbers satisfying the above condition is a. 8 b. 4 c. 12 d. 16 e. None of these 39. Two numbers are in the ratio of 15: 11. If their H.C.F is 13, then the numbers are a. 195,143 b. 15 , 11 c. 26, 13 d. Data inadequate e. None of these 40. Find the least number which when decreased by 4 is exactly divisible by 9, 12, 15 and 18

a. 180 b. 184 c. 176 d. Cannot be determined e. None of these 41. Find the least number which when divided by 12, 15, 20 and 24 leaves the same remainder 2 in each case a. 120 b. 122 c. 118 d. Cannot be determined e. None of these 42. The sum of two numbers is PQ and their difference is 1/7 of their sum. Find their HCF a. 7/6 (PQ) b.6/7 (PQ) c. 1/7 (PQ) d. 1/6 (PQ) e. None of these 43. The LCM of three numbers is 4752 and HCF is 6. If the two numbers are 48 and 66, then find the third number a. 36 b. 54 c. 42 d. 60 e. None of these 44. How many numbers between 200 and 300 which are exactly divisible by 6, 8, and 9? a. 2 b. 3 c. 4 d. 1 e. None of these 45. There are two electrical wires, one is 9 m 60 cm long aluminum wire and the other is 5 m 12 m long copper wire. Find the maximum length that can be equally cut from each wire in such a way that the total length of each wire is exactly divisible by it a. 64 cm b. 64 m c. 32 cm d. 128 cm e. None of these 46. Find the least number of girls, so that they can be arranged in the group of 15 or 20 or 30 a. 30 b. 60 c. 120 d. 180 e. 240

47. Find the least perfect square number which is exactly divisible by 3, 4, 5, 6 and 8 a. 6400 b. 14400 c. 6250 d. 3600 e. None of these 48. Find the greatest number less than 800, which is divisible by 8, 12, 28 a. 672 b. 660 c. 540 d. 720 e. None of these 49. Find the least number which when divided by 12, 15 and 20 leaves remaining 4, 7 and 12 respectively a. 50 b. 48 c. 52 d. 54 e. None of these 50. Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 but when divided by 9 leaves no remainder a. 1680 b. 187 c. 1683 d. 3366 e. None of these 51. Five balls begin to toll together and toll at intervals of 24, 40, 72 and 120 s. After what interval to time will they toll again together? a. 24 min. b. 48 min. c. 12 min. d. 72 min. e. None of these 52. Four wheels moving 12, 24, 20 and 30 revolutions in a minute starting at a certain point on the circumference downwards. After interval of time will they come together again in the same position? a. 20s b. 30s c. 1 min d. 45s e. None of these 53. The traffic lights at three different road crossings change after every 48.72 and 108 s respectively. If they change

simultaneously at 9 am, at what time will they change again simultaneously? a. 7 min 12 s b. 8 min c. 7 min 24 s d. 7 min e. None of these 54. Find the smallest four digit number that is exactly divisible by 8, 10 and 12 a. 1000 b. 80 c. 1080 d. 900 e. None of these 55. Find the greatest five digit number exactly divisible by 6, 8 and 12 a. 99984 b. 99900 c. 99800 d. 99884 e. None of these 56. Find the greatest number which will divide by 321, 428 and 535 exactly a. 107 b. 103 c. 101 d. 111 e. None of these 57. Find the greatest possible length which can be used to measure 4m 3cm, 4m 34cm and 4m 65cm exactly a. 31 m b. 31 cm c. 3.1 m d. 3.1 cm e. None of these 58. Find the least number of square tiles required to pave the floor of a room of 4 m 50 cm long and 5 m 25 cm broad a. 44 b. 42 c. 40 d. 80 e. None of these 59. Find the sum of the smallest four digit number and the largest five digit number a. 100999 b. 109999 c. 100099 d. 9999900 e. None of these

60. Five balls begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12. How many times they will toll together in one hour, excluding the one at the start? a. 6 b. 7 c. 8 d. 9 e. None of these 61. Among how many students, 175 bananas and 105 oranges can be equally divided? a. 70 b. 25 c. 35 d. 45 e. None of these 62. Find out the LCM of 234 , 532 , 745 , 1176 and 256 , 332 , 531 , 724 a. 256 , 332 , 532 , 745 , 1176 b. 256 , 332 , 532 , 724 c. 256 , 532 , 745 , 1176 d. 234 , 332 , 532 , 745 , 1176 e. None of these 63. What is the smallest whole number that is exactly divisible by a. 128 b. 132 c. 130 d. 145 e. None of these 64. The least perfect square which is divisible by each of the numbers 12, 15, 20 and 24 is a. 4900 b. 1600 c. 3600 d. 14400 e. None of these 65. The least positive integer which leave a remainder 2, when divided by each of the numbers 4, 6, 8, 12 and 16 a. 98 b. 50 c. 48 d. 52 e. None of these 66. The number of integers between 200 and 600 that are divisible by 2, 3, and 7 is

a. 6 b. 7 c. 9 d. 10 e. None of these 67. If three natural numbers, whose LCM is 360, are in the ratio 2:3:4, then the largest of them is a. 120 b. 60 c. 180 d. 240 e. None of these 68. The HCF of 168, 189 and 231 reduced by 8, gives a. 11 b. 13 c. 17 d. 21 e. None of these 69. The GCD and LCM of two numbers are 66 and 384 respectively. If the first number is divided by 2, the resulting answer is 66. The second number is a. 190 b. 192 c. 120 d. 90 e. None of these 70. The LCM and GCD of two numbers are 240 and 16 respectively. If the two numbers are in the ratio 3:5, the numbers are a. 16, 80 b. 48, 80 c. 12, 60 d. 6 , 10 e. None of these 71. The LCM of two numbers is 280 and the ratio of the numbers of 7:8. Find the numbers a. 35 and 40 b. 21 and 24 c. 28 and 32 d. 32 and 48 e. None of these

1. A 2. B 3. C 4. C 5. C 6. A 7. A 8. A 9. B 10. D 11. A 12. C 13. B 14. D 15. C 16. A 17. C 18. A 19. B 20. B 21. A 22. D 23. A 24. A 25. A 26. C 27. C 28. A 29. B 30. B 31. A 32. A 33. D 34. C 35. A 36. B 37. C 38. B 39. A 40. B 41. B 42. B 43. B 44. A 45. A 46. B 47. D 48. A 49. C 50. C 51. B 52. B 53. A 54. C 55. A 56. A 57. A 58. B 59. A 60. B 61. C 62. A 63. B 64. C 65. B 66. D 67. A 68. B 69. B 70. B 71. A