# H.C.F & L.C.M. - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to H.C.F & L.C.M.. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz. Q 1 - H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 49 is?

A - 360

B - 540

C - 180

D - 1260

### Explanation

```4 x 27 x 3125 = 22 x 33 x 55; 8 x 9 x 25 x 7 = 23 x 32 x 52 x 7;
16 x 81 x 5 x 11 x 49 = 24 x 34 x 5 x 72 x 11.
Therefore H.C.F = 180.```

Q 2 - The greatest number of four digits which is exactly divisible by 15, 25, 40, and 75 is?

A - 7000

B - 9650

C - 9600

D - 6500

### Explanation

```Greatest number of 4 digits is 9999. L.C.M  of 15, 25, 400 and 75 is 600.
On dividing 9999 by 600, the remainder  is 399.
Required number = (9999 - 399) = 9600.```

Q 3 - The least number, which when divided by 48, 60, 72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is?

A - 11115

B - 15110

C - 15120

D - 15210

### Explanation

```Here (48 - 38) = 10, (60 - 50) = 10, (72 - 62) = 10, (108 - 98) = 10 & (140 - 130) = 10
Therefore Required number = (L.C.M  of 48,60,72,108,140) - 10 = 15120 - 10 =15110.```

Q 4 - Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. the sum of the three numbers is?

A - 45

B - 85

C - 60

D - 65

### Explanation

```Since the numbers are co-prime they contain only 1 as the common factor. Also the given two products have the middle number in common.
So, the middle number = H.C.F of 551 and 1073 = 29;
First number = 551⁄29 = 19; Third number = 1073⁄29 = 37
required sum = (19 + 29 + 37) = 85.```

Q 5 - The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and pencils?

A - 91

B - 910

C - 1001

D - 1911

### Explanation

`Required number of students = H.C.F of 1001 and 910 = 91.`

Q 6 - The L.C.M. of two numbers is 72. Their H.C.F. is 12. If one number is 12, the other is

A - 24

B - 28

C - 32

D - 36

### Explanation

```Let the other number be X
HCF*LCM=Product of two numbers
12*72=24*X
⇒X=(12*72)/24=36```

Q 7 - Three number are in the ratio of 5: 6: 7 and their L.C.M. is 2100. Their H.C.F. is:

A - 40

B - 30

C - 20

D - 10

### Explanation

```Let the numbers be 5X, 6X and 7X
Then, their L.C.M. = 210X.
So, 210X = 2100 or X = 10.
The numbers are (5 x 10), (6 x 10) and (7 x 10).Hence, required H.C.F. = 10.```

Q 8 - The ratio of two numbers is 2:3. Having their L.C.M as 150, numbers are :

A - 30,40

B - 48,64

C - 50,75

D - none of these

### Explanation

```Let the numbers be  2x and 3x . Then, their L.C.M is 6x.
6x =  150    ⇒ x=  25
So, the numbers are 50 and 75.```

Q 9 - The ratio of two numbers is 15:11. Having their H.C.F as 13 ,numbers are:

A - 75, 55

B - 105, 77

C - 15,11

D - 195, 143

### Explanation

```Let the numbers be 15x  and 11x . Then , their H.C.F is x.
∴ x= 13 and so the numbers are (15*13, 11*13) i.e , 195, 143```

Q 10 - What is the greatest length possible of a scale that can be used to measure exactly 3m , 5m 10 cm and 12m 90 cm length?

A - 10 cm

B - 20 cm

C - 25 cm

D - 30 cm

`Required length  = H.C.F of 300 cm, 510 cm, 1290 cm =30 cm`