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Aptitude Problems on L.C.M and H.C.F Set 2

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1. The product of two numbers is 2025 and their HCF is 15 their LCM is:




2. The least number which when divided by 16, 18 and 21, leave the remainder 3, 5 and 8 respectively is:




3. The least square number which divides 8, 12 and 18 is?




4. The least number which when divided by 8, 12 and 16, leave in each remainder 3, is?




5. The least number which when add 3 to it, completely divided 8, 12 and 18 is?




6. Four bells begin to toll together respectively at the intervals of 8, 10, 12 and 16 seconds. After how many seconds will they toll together again?




7. The product of two digits number is 2160 and their HCF is 12. The numbers are:




8. The greatest number of five digits which is divisible by 32, 36, 40, 42 and 48 is:




9. The least number of four digits which is divisible by 4, 6, 8 and 10 is?




10. The greatest number of four digits that have 144 for their HCF is?




11. The least number of five digits that have 144 their HCF is?




12. The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is:




13. A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is?




14. The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?




15. Five bells first begin to toll together and then at intervals of 5, 10, 15, 20 and 25 seconds respectively. After what interval of time will they toll again together?




16. HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?




17. Least perfect square number, exactly divisible by 21, 36 and 56 is?




18. In finding the HCF of two numbers, the last divisor was 41 and the successive quotients, starting from the first, where 2, 4 and 2. The numbers are?




19. A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?




20. An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?




21. Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case?




22. Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?




23. A merchant has three different types of milk: 435 liters, 493 liters and 551 liters. Find the least number of casks of equal size required to store all the milk without mixing.




24. A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box?




25. Find the size of the largest square slabs which can be paved on the floor of a room 5 meters 44 cm long and 3 meters 74 cm broad?




26. A room is 4 meters 37 cm long and 3 meters 23cm broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose?




27. How many minimum number's of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side?




28. There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?




29. There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number?




30. Two numbers 4242 and 2903 when divided by a certain number of three digits, leave the same remainder. Find the number?




31. The wheels revolve round a common horizontal axis. They make 15, 20 and 48 revolutions in a minute respectively. Starting with a certain point on the circumference down wards. After what interval of time will they come together in the same position?




32. What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively?




33. Find the least number which when divided by 35 leaves remainder 25, when divided by 25 leaves remainder 15 and when divided by 15 leaves remainder 5?




34. Find the greatest number of four digits which when divided by 10, 15, 21 and 28 leaves 4, 9, 15 and 22 as remainders respectively?




35. A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?




36. Find the least number which when divide by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 7 leaves no remainder?




37. Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainders respectively?




38. Find the least number which when divided by 6, 7, 8, 9 and 10 leaves 1, 2, 3, 4 and 5 as remainders respectively, but when divided by 19 leaves no remainder?




39. Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point?




40. Find the least square number which is divisible by 10, 12, 15 and 18?




41. A gardener was asked a plant flowers in a row containing equal number of plants. He tried to plant 6, 8, 10 and 12 in each row, but 5 plants left in each case. When he planted 13 in a row, no plant was left. Find the number of plants with him?




42. Find the smallest number which when increased by 5, divisible by 6, 9, 15, 20 and 24?




43. Find the greatest 4-digit number exactly divisible by 3, 4 and 5?




44. Find the lowest 4-digit number which when divided by 3, 4 or 5 leaves a remainder of 2 in each case?




45. Find the greatest number that exactly divides 35, 91 and 840?




46. Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?




47. Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case?




48. A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?




49. 252 can be expressed as a product of primes as:




50. Which of the following has most number of divisors?




51. 1095/1168 when expressed in simplest form is:




52. H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is:




53. Find the highest common factor of 36 and 84.




54. Find the lowest common multiple of 24, 36 and 40.




55. The G.C.D of 1.08, 0.36 and 0.9 is




56. H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is:




57. Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are:




58. The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is:




59. The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:




60. The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is:




61. The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is:




62. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is :




63. The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is:




64. Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:




65. The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is:




66. The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is:




67. If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to:




68. Product of two co-prime numbers is 117. Their L.C.M should be:




69. The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?




70. The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:




71. Which of the following fractions is the largest?




72. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?




73. The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is:




74. The least number of four digits which is divisible by 15, 25, 40 and 75 is:




75. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:




76. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?




77. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:




78. Which of the following has the most number of divisors?




79. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:




80. Greatest Common Divisor of two numbers is 8 while their Least Common Multiple is 144. Find the other number if one number is 16.