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Home Aptitude Problems on H.C.F and L.C.M Comments

  • Question
  • The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:


  • Options
  • A. 1677
  • B. 1683
  • C. 2523
  • D. 3363

  • Correct Answer
  • 1683 

    Explanation
    L.C.M. of 5, 6, 7, 8 = 840.

    ∴ Required number is of the form 840k + 3

    Least value of k for which (840k + 3) is divisible by 9 is k = 2.

    ∴ Required number = (840 x 2 + 3) = 1683.


  • Problems on H.C.F and L.C.M


    Search Results


    • 1. Reduce 128352/238368 to its lowest terms

    • Options
    • A. 34
    • B. 513
    • C. 713
    • D. 913
    • Discuss
    • 2. 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 again at the starting point?

    • Options
    • A. 26 minutes and 18 seconds
    • B. 42 minutes and 36 seconds
    • C. 45 minutes
    • D. 46 minutes and 12 seconds
    • Discuss
    • 3. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

    • Options
    • A. 1008
    • B. 1015
    • C. 1022
    • D. 1032
    • Discuss
    • 4. Find the lowest common multiple of 24, 36 and 40.

    • Options
    • A. 120
    • B. 240
    • C. 360
    • D. 480
    • Discuss
    • 5. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:

    • Options
    • A. 12
    • B. 16
    • C. 24
    • D. 48
    • Discuss
    • 6. Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

    • Options
    • A. 40
    • B. 80
    • C. 120
    • D. 200
    • Discuss
    • 7. What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?

    • Options
    • A. 196
    • B. 630
    • C. 1260
    • D. 2520
    • Discuss
    • 8. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

    • Options
    • A. 74
    • B. 94
    • C. 184
    • D. 364
    • Discuss
    • 9. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 10. 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?

    • Options
    • A. 4
    • B. 10
    • C. 15
    • D. 16
    • Discuss


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