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

  • Question
  • 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

  • Correct Answer
  • 364 

    Explanation
    L.C.M. of 6, 9, 15 and 18 is 90.

    Let required number be 90k + 4, which is multiple of 7.

    Least value of k for which (90k + 4) is divisible by 7 is k = 4.

    ∴ Required number = (90 x 4) + 4   = 364.


  • Problems on H.C.F and L.C.M


    Search Results


    • 1. 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
    • 2. 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
    • 3. 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
    • Discuss
    • 4. Reduce 128352/238368 to its lowest terms

    • Options
    • A. 34
    • B. 513
    • C. 713
    • D. 913
    • Discuss
    • 5. 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
    • 6. 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
    • 7. 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
    • 8. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

    • Options
    • A. 4
    • B. 5
    • C. 6
    • D. 8
    • Discuss
    • 9. 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 reciprocals of the numbers is equal to:

    • Options
    • A. 55601
    • B. 60155
    • C. 11120
    • D. 12011
    • Discuss
    • 10. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

    • Options
    • A. 101
    • B. 107
    • C. 111
    • D. 185
    • Discuss


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