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



Advertisements


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.

Questions and Answers

Q 1 - 252 can be expressed as a product of primes as

A - 3 x 3 x 3 x 3 x 7

B - 2 x 2 x 3 x 3 x 7

C - 2 x 2 x 2 x 3 x 7

D - 2 x 3 x 3 x 3 x 7

Answer : B

Explanation

Clearly, 252 = 2 x 2 x 3 x 3 x 7.

Q 2 - Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are?

A - 11,25,35

B - 12,24,36

C - 11,15,16

D - 12,25,36

Answer : B

Explanation

Let the required numbers be z, 2z, and 3z.
Then, their H.C.F = z 
 So, z = 12.
Therefore The number are 12, 24 and 36.

Q 3 - Find the highest common factor of 36 and 84.

A - 5

B - 6

C - 4

D - 12

Answer : D

Explanation

36 = 22 x 32 84 = 22 x 3 x 7.
Therefore H.C.F = 22 x 3 = 12.

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

Answer : B

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 = 55129 = 19; Third number = 107329 = 37
required sum = (19 + 29 + 37) = 85.

Q 5 - The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?

A - 60

B - 24

C - 48

D - 56

Answer : A

Explanation

H.C.F of two numbers divide their L.C.M exactly. Clearly 8 is not a factor of 60.

Q 6 - Three piece of timber 35m, 42m, 70m long have to be divided into planks of the same length. What is the greatest possible length of each cloth?

A - 35

B - 5

C - 6

D - 7

Answer : D

Explanation

The maximum possible length = (G.C.D. of 35, 42, 70) =7

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

Answer : D

Explanation

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

Q 8 - The L.C.M of two numbers is 12 times their H.C.F and sum of H.C.F and L.C.M is 403. Having one number as 93, find the other one.

A - 128

B - 124

C - 134

D - None of these

Answer : B

Explanation

Let L.C.M =x and H.C.F = y . Then,
X= 12y  and x+y = 403 ⇒12y+y = 403 ⇒13y= 403 ⇒y = 403/13 = 31
∴ x=   (12*31 ) = 372
Let the other number be z. then,
372*31 = 93*z ⇒ z = (372*31)/93  =124
Hence , the other number is 124 .

Q 9 - If ratio of two numbers is 2:3 and the product of their H.C.F and L.C.M is 33750, find the sum of the numbers:

A - 250

B - 325

C - 375

D - 425

Answer : C

Explanation

Let the numbers be 2x and 3x.  Then, H.C.F = x and L.C.M = 6x
∴ 6x*x = 33750  ⇒ x2 = 5625   ⇒ &sqrt;5625= 75
So, the numbers are 150  and 225 . Their sum is 375.

Q 10 - H.C.F of 3240, 3600 and x is 36 and their L.C.M is (2⁴*3⁵*52*72).Find x.

A - 2⁵*52* 72

B - 23*3⁵*72

C - 22*3⁵*72

D - 22* 53*72

Answer : C

Explanation

3200 = 23* 3⁴*5
H.C.F = 36= 22*32
3600 =  2⁴*32* 52
L.C.M = 2⁴* 3⁵*52* 72
∴ 3rd number must have 22*32 as its factor.
∴ 3rd number  = 22* 3⁵*72


aptitude_hcf_lcm.htm

Advertisements