Practice Test for Find LCM& HCF

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  1. Find the largest possible length of a scale that can measure exactly 90 cm, 120 cm, and 150 cm.
  2. A number when dividing 729, 1035, and 1413 leaves remainder 3. Find that number.
  3. The divisor of 78 and 89 leaves different remainders 6 and 7. Find the divisor.
  4. A school has 72 boys and 108 girls. They are to be seated in rows such that each row has the same number of students. Find the greatest number of students that can be seated in each row.
  5. Find the least number which when divided by 9, 11, and 13 leaves remainders 4, 6, and 8.
  6. Find the divisor when 945, 1269, and 1581 leave remainder 9.
  7. A fruit seller has 48 apples and 72 oranges. He wants to make fruit baskets with equal numbers of apples and oranges. Find the maximum number of baskets he can prepare.
  8. Find the greatest divisor of 437, 697, and 1069 if they leave the same remainder.
  9. Find the smallest number which when divided by 6, 8, and 11 leaves remainders 3, 5, and 7.
  10. The numbers 2431, 3131, and 3531 leave remainder 1. Find the divisor.
  11. Find the least number which when divided by 12, 20, and 25 leaves remainders 6, 14, and 19.
  12. A number divides 356, 476, and 596 leaving remainder 16. Find the number.
  13. A number when divided by 11, 13, and 17 leaves remainder 2. Find the least such number.
  14. A gardener has 48 rose plants and 60 tulip plants. He wants to plant them in rows such that each row has the same number of plants of one kind. Find the maximum number of rows he can make.
  15. Find the divisor when 437, 697, and 1069 are divided by it leaving remainder 9.
  16. Find the least number which when divided by 8, 9, and 11 leaves remainders 2, 3, and 5.
  17. The numbers 121, 245, and 361 when divided by a number leave remainder 1. Find the number.
  18. The greatest number dividing 999, 1299, and 1599 leaving the same remainder is what?
  19. Find the smallest number which when divided by 5, 9, and 11 leaves remainders 1, 5, and 7.
  20. A number divides 1234, 1654, and 2044 leaving remainder 4. Find the divisor.
  21. Two ropes of lengths 18 m and 24 m are to be cut into pieces of equal length. Find the greatest length of each piece.
  22. Find the least number which when divided by 8, 10, and 12 leaves remainders 5, 7, and 9.
  23. The numbers 158, 398, and 798 leave remainder 2 when divided by a number. Find the divisor.
  24. Find the smallest number which when divided by 10, 12, and 15 leaves remainder 7.
  25. Find the greatest number which divides 246, 492, and 738 leaving the same remainder each time.
  26. Find the least number which when divided by 9, 12, and 16 leaves remainders 4, 8, and 12.
  27. A number leaves remainder 2 when dividing 50, and remainder 5 when dividing 65. Find the number.
  28. When 121, 245, and 361 are divided by a number, the remainders are equal. Find the greatest possible divisor.
  29. The numbers 1555, 1805, and 2105 leave remainder 5 when divided. Find the divisor.
  30. Find the smallest number which when divided by 14, 18, and 20 leaves remainders 6, 10, and 12.
  31. A number divides 123 and 234 leaving remainders 3 and 6. Find the divisor.
  32. The numbers 2431, 3131, and 3531 leaving the same remainder is what?
  33. Find the least number which when divided by 12, 18, and 24 leaves remainders 7, 13, and 19.
  34. Find the least number which when divided by 3, 4, and 5 leaves remainder 2.
  35. A number divides 75 and 92 leaving remainders 3 and 2. Find the divisor.
  36. A rectangular garden has dimensions 72 m by 90 m. Find the largest square tiles that can pave the garden exactly.
  37. Find the smallest number which when divided by 9, 13, and 17 leaves remainders 2, 6, and 10.
  38. Find the smallest number which when divided by 7, 9, and 10 leaves remainders 3, 5, and 7.
  39. The greatest number dividing 2431, 3131, and 3531 leaving the same remainder is what?
  40. A number when divided by 7, 9, and 11 leaves remainder 4. Find the least such number.
  41. Find the smallest number which when divided by 11, 13, and 17 leaves remainders 6, 8, and 12.
  42. Find the least number which when divided by 10, 18, and 25 leaves remainders 4, 10, and 15.
  43. The length and breadth of a hall are 108 m and 135 m. Find the largest tile size which can exactly cover the floor without cutting.
  44. Find the smallest number which when divided by 6, 10, and 14 leaves remainders 2, 4, and 6.
  45. A number when divided by 3, 5, and 7 leaves remainder 2. Find the least such number.
  46. Find the divisor if 234, 504, and 774 leave remainder 4 when divided.
  47. Find the least number which when divided by 6, 8, and 10 leaves remainder 3.
  48. Find the smallest number which when divided by 16, 18, and 20 leaves remainders 8, 10, and 12.
  49. Three pieces of wood are 84 cm, 98 cm, and 112 cm long. Find the greatest length of a measuring rod that can measure each piece exactly.
  50. The numbers 175, 275, and 475 leave remainder 5 when divided. Find the divisor.
  51. Find the smallest number which when divided by 7, 11, and 13 leaves remainders 3, 7, and 9.
  52. Find the least number which when divided by 8, 12, and 16 leaves remainder 5.
  53. A milkman has 60 liters of milk and 84 liters of water. He wants to store them in containers of equal capacity. Find the maximum capacity of each container.
  54. A number leaves remainder 7 when divided by 8, 10, and 12. Find the least such number.
  55. When 187, 319, and 391 are divided by a number, they leave a remainder 7. Find the divisor.
  56. The greatest number that divides 1001, 1257, and 1805 leaving the same remainder is what?
  57. Find the least number which when divided by 4, 6, and 8 leaves remainders 1, 3, and 5.
  58. A number when dividing 340, 580, and 820 leaves the same remainder. Find the divisor.
  59. Find the greatest divisor of 246, 492, and 738 if each leaves remainder 6.
  60. Find the smallest number which when divided by 9, 10, and 12 leaves remainders 5, 6, and 7.
  61. Find the least number which when divided by 7, 12, and 15 leaves remainders 2, 7, and 10.
  62. When a number divides 56 and 94, the remainders are 4 and 6. Find the divisor.
  63. Find the smallest number which when divided by 15, 18, and 21 leaves remainders 7, 10, and 13.
  64. Find the smallest number which when divided by 25, 30, and 40 leaves remainder 5.
  65. The numbers 201, 421, and 781 leave the same remainder. Find the divisor.
  66. When a number divides 67 and 97, the remainders are 3 and 7 respectively. Find the greatest number.
  67. The numbers 192, 272, and 352 leave remainder 8 when divided by a number. Find it.
  68. Find the least number which when divided by 12, 15, and 20 leaves remainder 4.
  69. Find the smallest number which when divided by 5, 6, and 7 leaves remainders 1, 2, and 3.
  70. The numbers 1001, 1257, and 1805 leave remainder 5 when divided. Find the divisor.
  71. Find the smallest number which when divided by 14, 16, and 18 leaves remainders 4, 6, and 8.
  72. Find the least number which when divided by 9, 12, and 15 leaves remainder 6.

Answer:

  1. 30
  2. 6
  3. 11
  4. 36
  5. 128
  6. 108
  7. 24
  8. 87
  9. 419
  10. 700
  11. 100
  12. 40
  13. 243
  14. 12
  15. 87
  16. 443
  17. 120
  18. 300
  19. 491
  20. 420
  21. 6
  22. 399
  23. 240
  24. 127
  25. 246
  26. 144
  27. 15
  28. 120
  29. 250
  30. 348
  31. 37
  32. 700
  33. 38
  34. 2
  35. 23
  36. 18
  37. 252
  38. 463
  39. 613
  40. 90
  41. 692
  42. 132
  43. 325
  44. 27
  45. 90
  46. 257
  47. 77
  48. 30
  49. 270
  50. 28
  51. 14
  52. 500
  53. 819
  54. 133
  55. 84
  56. 64
  57. 8
  58. 381
  59. 61
  60. 4
  61. 20
  62. 152
  63. 8
  64. 995
  65. 399
  66. 23
  67. 15
  68. 385
  69. 990
  70. 72
  71. 84
  72. 46

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