LCM and HCF questions for Competitive Exams. Important selected MCQ question answer with solution for the study of SSC CGL, CHSL, CPO, GD, NRA CET, RRB, UPSSSC PET and Mains , Bank and other Govt jobs exams.

## Topic wise LCM and HCF Questions

#### Type-I : Questions Based on Formula (LCM × HCF = First Number × Second Number)

**Q.1: The LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 189, the other number is**1) 297

2) 584

3) 189

4) 216

**Q.2: The product of two co-prime numbers is 117. Then their LCM is**

1) 117

2) 9

3) 13

4) 39

**Q.3: The LCM of three different numbers is 120. Which of the following cannot be their HCF?**

1) 8

2) 12

3) 24

4) 35

**Q.4: The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is**1) 5

2) 25

3) 100

4) 125

**Q.5: The product of two numbers is 216. If the HCF is 6, then their LCM is**1) 72

2) 60

3) 48

4) 36

**Q.6: The product of two numbers is 4107. If the HCF of the numbers is 37, then a greater number is**1) 185

2) 111

3) 107

4) 101

**Q.7: LCM of two numbers is 225 and their HCF is 5. If one number is 25, then the other number will be**1) 5

2) 25

3) 45

4) 225

**Q.8: The LCM of two numbers is 864 and their HCF is 144. If one of the number is 288, then the other number is**1) 576

2) 1296

3) 432

4) 144

LCM and HCF MCQ Questions

### Type-II: Finding the LCM of the Numbers

**Q.9: Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.**

1) 183

2) 243

3) 483

4) 723

**Q.10: The greatest 4-digit number exactly divisible by 10, 15, 201 is**

1) 9990

2) 9960

3) 9980

4) 9995

**Q.11: The bells begin to toll together and they toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again?**

1) 72 Seconds

2) 612 Seconds

3) 504 Seconds

4) 318 Seconds

**Q.12: The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is**

1) 9763

2) 9764

3) 9766

4) 9765

**Q.13: A, B and C start running at the same time and at the same point in the same direction in a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds. After what time will they meet again at the starting point?**

1) 26 minutes 18 seconds

2) 42 minutes 36 seconds

3) 45 minutes

4) 46 minutes 12 seconds

**Q.14: The least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder is**

1) 17004

2) 18000

3) 18002

4) 18004

**Q.15: 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**

1) 1677

2) 1683

3) 2523

4) 3363

**Q.16: The smallest perfect square divisible by each of 6, 12 and 18 is **

1) 196

2) 144

3) 108

4) 36

**Q.17: The smallest number, which, when divided by 12 or 10 or 8, leaves remainder 6 in each case, is**

1) 246

2) 186

3) 126

4) 66

**Q.18: The greatest number of four digits which when divided by 12, 16 and 24 leave remainders 2, 6 and 14 respectively is**

1) 9974

2) 9970

3) 9807

4) 9998

**Q.19: The smallest number, which when increased by 5 is divisible by each of 24, 32, 36 and 564 is**

1) 869

2) 859

3) 4320

4) 427

**Q.20: What is the LCM of 1.08, 0.36 and 0.9**1) 1.08

2) 0.9

3) 10.8

4) 5.4

LCM and HCF Questions for Competitive Exams

### Type-III: Finding the HCF of Numbers

**Q.21: The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively is**

1) 136

2) 168

3) 42

4) 84

**Q.22: The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively is**

1) 15

2) 16

3) 19

4) 20

**Q.23: Three tankers contain 403 litres, 434 liters and 465 liters of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers the exact number of times is**

1) 31 Litres

2) 62 Litres

3) 41 Litres

4) 84 Litres

**Q.24: 84 Maths books, 90 Physics books and 120 Chemistry books have to be stacked topic-wise. How many books will be there in each stack so that each stack will have the same height too?**

1) 12

2) 18

3) 6

4) 21

**Q.25: A milk vendor has 21 liters of cow milk, 42 liters of toned milk and 63 liters of double toned milk. If he wants to pack them in cans so that each can contain the same liters of milk and does not want to mix any two kinds of milk in a can, then the least number of cans required is**

1) 3

2) 6

3) 9

4) 12

**Q.26: Which is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?**

1) 840

2) 841

3) 820

4) 814

**Q.27: A milkman has 75 liters of milk in one can and 45 liters in another. The maximum capacity of container which can measure the milk of either container the exact number of times is**

1) 1 Litre

2) 5 Litres

3) 15 Litres

4) 25 Litres

**Q.28: The greatest number, which when divided by 989 and 1327 leave remainders 5 and 7 respectively is**

1) 8

2) 16

3) 24

4) 32

**Q.29: The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens andsame number of pencils is**

1) 91

2) 910

3) 1001

4) 1911

LCM and HCF Questions for Competitive Exams

### Type-IV: Ratio of the Numbers : LCM and HCF Questions

**Q.30: The HCF and LCM of two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4, then the largest of the two numbers is**

1) 12

2) 108

3) 48

4) 84

**Q.31: If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two numbers is**

1) yz

2) xz/y

3) xy/z

4) xyz

**Q.32:Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are**

1) 12, 24, 36

2) 5, 10, 15

3) 4, 8, 12

4) 10, 20, 30

Q.33: The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is

Q.33: The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is

1) 10

2) 60

3) 15

4) 12

**Q.34: Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is**

1) 48

2) 42

3) 36

4) 24

**Q.35: The ratio of two numbers is 4 : 5 and their HCF is 8. Then their LCM is**

1) 130

2) 140

3) 150

4) 160

**Q.36: The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is**

1) 28

2) 32

3) 40

4) 64

**Q.37: The ratio of two numbers is 4 : 5 and their LCM is 120. The numbers are**

1) 30 and 40

2) 40 and 32

3) 24 and 30

4) 36 and 20

**Q.38: If the ratio of two numbers is 2 : 3 and their LCM is 54, then the sum of the two numbers is**

1) 5

2) 15

3) 45

4) 270

**Q.39: The LCM and the HCF of the numbers 28 and 42 are in the ratio**

1) 6:1

2) 2:3

3) 3:2

4) 7:2

### Type-V : Addition, Subtraction, Multiplication and Division of Numbers

**Q.40: The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is**

1) 4023

2) 4032

3) 4302

4) 4203

**Q.41: A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is**

1) 1451

2) 1641

3) 1712

4) 1523

**Q.42: The greatest four-digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 is**

1) 9828

2) 9288

3) 9882

4) 9928

**Q.43: Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is**

1) 7

2) 5

3) 6

4) 4

**Q.44: The number between 3000 and 4000 which is exactly divisible by 30, 36 and 80 is**

1) 3625

2) 3250

3) 3500

4) 3600

**Q.45: The LCM of two numbers is 44 times of their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is**

1) 1100

2) 975

3) 900

4) 800

**Q.46: The LCM of two numbers is 20 times their HCF. The sum of HCF and LCM is 2520. If one of the number is 480, then the other number is**

1) 400

2) 480

3) 520

4) 600

**Q.47: Which least number should be subtracted from the number 36798 so that the new number is completely divisible by 78?**

1) 18

2) 60

3) 38

4) 68

Thanks for attempt LCM and HCF MCQ Questions for Competitive Exams

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