Aptitude Questions on LCM-HCF

  1. The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
    A. 24
    B. 48
    C. 56
    D. 60
  2. D. 60
    H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60
  3. If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.
    A. 25
    B. 30
    C. 50
    D. 125
  4. A. 25
    H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25
  5. LCM of 1/3, 5/6, 5/4, 10/7 is:
    A. 10/11
    B. 11/10
    C. 10/7
    D. 10
  6. D. 10
    LCM of numerators = 10
    HCF of denominators = 1
    => 10/1 = 10
  7. HCF of 3/16, 5/12, 7/8 is:
    A. 1/48
    B. 2/47
    C. 3/47
    D. 5/48
  8. A. 1/48
    HCF of numerators = 1
    LCM of denominators = 48
    => 1/48
  9. The least square number which divides 8, 12 and 18 is?
    A. 64
    B. 100
    C. 144
    D. 196
  10. C. 144
    LCM = 72
    72 * 2 = 144
  11. The least number which when divided by 8, 12 and 16, leave in each remainder 3, is?
    A. 51
    B. 61
    C. 69
    D. 71
  12. A. 51
    LCM = 48 + 3 = 51
  13. The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is?
    A. 1261
    B. 1265
    C. 1267
    D. 1269
  14. C. 1267
    LCM = 1260
    1260 + 7 = 1267
  15. 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?
    A. 35
    B. 37
    C. 39
    D. 40
  16. B. 37
    HCF of 1189, 1073 = 29
    1073/29 = 37
  17. 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?
    A. 2
    B. 3
    C. 4
    D. 5
  18. B. 3
    HCF of 4956, 3894 = 354
    (4956 - 3894)/354 = 3
  19. 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.
    A. 45
    B. 47
    C. 51
    D. 61
  20. C. 51
    HCF of 435, 493, 551 = 29
    (453/29) + (493/29) + (551/29) = 51