# 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 - Reduce 128352238368 to its lowest terms.

A - 713

B - 34

C - 513

D - 913

### Explanation

Q 2 - Which of the following fractions is the largest?

A - 78

B - 1316

C - 3140

D - 6380

### Explanation

```L.C.M of 8, 16, 40 and 80 = 80
7⁄8 = 70⁄80; 13⁄16 = 65⁄80; 31⁄40 = 62⁄80
Since 70⁄80 > 63⁄80 > 65⁄80 > 62⁄80
7⁄8 > 63⁄80 > 13⁄16 > 31⁄40
S0, 7⁄8 is the largest.```

Q 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?

A - 1677

B - 2535

C - 1683

D - 3363

### Explanation

```L.C.M of 5,6,7,8 = 840
Therefore Required number is of the form (840k + 3)
Least value of k which (840k + 3) is divisible by 9 is k = 2.
Therefore Required number = (840 x 2 + 3) = 1683```

Q 4 - The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is?

A - 279

B - 308

C - 283

D - 318

### Explanation

`Other number = 11 x 7700⁄275 = 308`

Q 5 - A rectangular courtyard 3.78 meters long and 5.25 meters wide is to be paved exactly with square titles all of the same size. What is the largest size of the tile which could be used for the purpose?

A - 21 cms

B - 14 cms

C - 42 cms

D - none of the above.

### Explanation

`Largest size of the tile = H.C.F of 378 cm and 525 cm = 21 cms.`

Q 6 - Find the L.C.M. of 2/3, 2/5 and 2/7.

A - 2

B - 2/3

C - 2/5

D - 2/7

### Explanation

```L.C.M. of given fractions =  (L.C.M.of numerators)/(H.C.F.of denominators)=2/1=2
(L.C.M.of numerators = 2  H.C.F.of denominators =1)```

Q 7 - Which greatest possible length can be used to measure exactly 165 cm, 330 cm and 440 cm.

A - 5

B - 15

C - 50

D - 55

### Explanation

`HCF of 165 cm, 330 cm and 440 cm is 55 cm.`

Q 8 - H.C.F and L.C.M of two 3-digit numbers are 29 and 4147 respectively. What is the sum of the numbers?

A - 666

B - 669

C - 696

D - 966

### Explanation

```Let the numbers be 29a and 29 b , where a and b  are co-primes.
Then, 29 a * 29 b + 29*147 ⇒ ab + (29*4147)/(29*29)= 143
co-primes with product 143 are 11  and 13.
∴ numbers are (29*11,   29* 13) i.e ,  319, 377
Their sum = (319+377)= 696```

Q 9 - If the H.C.F of two numbers is 8. Then following number cannot be the L.C.M of these numbers.

A - 24

B - 48

C - 56

D - 60

### Explanation

```The H.C.F of two numbers always divides their L.C.M.
Since 8 does not divide 60, so, 60 cannot be their L.C.M.```

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`