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HCF and LCM - II (TSICET)

Practice problems on Highest Common Factor (HCF) and Least Common Multiple (LCM) including applications with remainders, number relationships, and divisibility rules.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Find the greatest number that will divide 251, 326 and 194, leaving remainders 1, 6 and 2, respectively.

  1. 60
  2. 64
  3. 65
  4. 54
  5. 50
Question 2 Multiple Choice (Single Answer)

Find the smallest number which when decreased by 9 becomes exactly divisible by 30, 32 and 42.

  1. 3369
  2. 3370
  3. 3375
  4. 3372
  5. 3368
Question 3 Multiple Choice (Single Answer)

The HCF and LCM of two numbers are 14 and 168, respectively. If one of the numbers is 48, then find the second number.

  1. 49
  2. 56
  3. 84
  4. 63
  5. 35
Question 4 Multiple Choice (Single Answer)

Find the least number which when divided by 36, 16, 24 and 48 leaves the remainder 7 in each case.

  1. 295
  2. 294
  3. 290
  4. 296
  5. 293
Question 5 Multiple Choice (Single Answer)

There are two types of wires, one is 2.40 m long and the second is 3.20 m long. Find the maximum length that can be equally cut from each wire in such a way that the total length of the wire is exactly divisible by it.

  1. 80 cm
  2. 70 cm
  3. 75 cm
  4. 90 cm
  5. 95 cm
Question 6 Multiple Choice (Single Answer)

Find the smallest 3-digit number such that when it is divided by 8, 16, 24 and 36, it leaves a remainder of 11 in each case.

  1. 1020
  2. 1024
  3. 1030
  4. 1029
  5. 1019
Question 7 Multiple Choice (Single Answer)

Find the greatest 4-digit number which is divisible by 78.

  1. 9994
  2. 9985
  3. 9984
  4. 9980
  5. 9990
Question 8 Multiple Choice (Single Answer)

The HCF of two numbers is 21 and their difference is 63. Find the numbers.

  1. 42, 27
  2. 84, 21
  3. 82, 93
  4. 105, 165
  5. 63, 27
Question 9 Multiple Choice (Single Answer)

The ratio of three numbers is 2 : 5 : 3. If their HCF is 9, then find the LCM of these numbers.

  1. 290
  2. 270
  3. 240
  4. 300
  5. 330
Question 10 Multiple Choice (Single Answer)

The LCM of two numbers is 108 and their HCF is 3. If the sum of the numbers is 39, then find the ratio of the two numbers.

  1. 4 : 9
  2. 2 : 3
  3. 5 : 4
  4. 3 : 4
  5. 5 : 6
Question 11 Multiple Choice (Single Answer)

Find the smallest number which becomes exactly divisible by 23, 29 and 21 when 5000 is subtracted from it.

  1. 25000
  2. 24660
  3. 25667
  4. 34667
  5. 25600
Question 12 Multiple Choice (Single Answer)

Find the least number which when divided by 65, 55 and 45 leaves the remainders 51, 41 and 31, respectively.

  1. 6400
  2. 6420
  3. 6424
  4. 6421
  5. 6425
Question 13 Multiple Choice (Single Answer)

The sum of two numbers is 56 and their difference is 8. Find the LCM of the two numbers.

  1. 96
  2. 48
  3. 72
  4. 64
  5. 80
Question 14 Multiple Choice (Single Answer)

Find a number between 200 and 400 which when divided by 35, 14 and 21 leaves 5 as a remainder in each case.

  1. 220
  2. 215
  3. 225
  4. 315
  5. 335
Question 15 Multiple Choice (Single Answer)

Find the greatest 4-digit number that is exactly divisible by 12, 27 and 9.

  1. 9828
  2. 9712
  3. 9946
  4. 9936
  5. 9966
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