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



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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 - Which of the following has most number of divisors?

A - 112

B - 176

C - 175

D - 170

Answer : B

Explanation

99 = 1 x 3 x 3 x 11;
101 = 1 x 101;
176 = 1 x 2 x 2 x 2 x 2 x 11;
182 = 1 x 2 x 7 x 13.
So, divisor of 99 are 1, 3, 9, 11, 33, 99
divisor of 101 are 1, 101
divisor of 176 are 1, 2, 4, 8, 16, 22, 44, 88, 176
divisor of 182 are 1, 7, 2, 13, 14, 26, 91, 182
Hence 176 has the most number of divisors.

Q 2 - The G.C.D of 1.08, 0.36 and 0.9 is?

A - 0.108

B - 0.9

C - 0.03

D - 0.18

Answer : B

Explanation

Given numbers are 1.08, 0.36 and 0.9. H.C.F of 108, 36 and 90 is 18.
H.C.F of given numbers is 0.18.

Q 3 - The least number which should be added to 2497 so that the sum is exactly divisible by 5,6,4 and 3 is?

A - 20

B - 23

C - 25

D - 30

Answer : B

Explanation

L.C.M of 5,6,4 and 3 = 60 
 On dividing 2497 by 60, remainder is 37. 
 Therefore Number to be added = (60 - 37) = 23.

Q 4 - Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is?

A - 10

B - 20

C - 30

D - 40

Answer : D

Explanation

Let the numbers be 3z, 4z, and 5z. then their L.C.M = 60z 
 So, 60z = 2400 or z = 40.
Therefore the numbers are (3 x 40), (4 x 40), (5 x 40).
Hence the required H.C.F = 40.

Q 5 - The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95cm is?

A - 25 cms

B - 35 cms

C - 15 cms

D - 42 cms

Answer : B

Explanation

Required length = H.C.F of 700, 385, 1295  = 35 cms.

Q 6 - Find the least number which when divided separately by 13, 26, 39 and 52 leaves 5 as remainder in each case.

A - 156

B - 150

C - 161

D - 166

Answer : C

Explanation

Required number = L.C.M. of (13, 26,39 and 52) +5
= 156 + 5 = 161

Q 7 - H.C.F. of two numbers is 12 and their L.C.M is 72. If the difference between the numbers is 24, their sum is

A - 36

B - 42

C - 48

D - 54

Answer : C

Explanation

Let the numbers be X & Y
HCF*LCM=Product of two numbers =XY=12x72=864
XY=864 -------- (1)
Given X-Y=24   -------- (2)
On solving 1 & 2 we get X=12 Y=36
Their sum = 12+36=48

Q 8 - The sum of two numbers is 45 and difference is 1/9 of their sum. What is their L.C.M:

A - 100

B - 150

C - 200

D - 250

Answer : A

Explanation

Let the numbers be x and y . Then,
{x+y= 45  , x= (1/9*45)= 5} ⇒x = 25, y =20
L.C.M of 25 and 20 = (5*5*4)= 100

Q 9 - H.C.F and L.C.F of two numbers x and y are 3 and 105 respectively. If x+y=36 then figure out 1/x + 1/y.

A - 35

B - 3/5

C - 4/3

D - 4/35

Answer : D

Explanation

We have X *y =3 *105 ⇒ xy = 315
∴  x+y/xy =36/315  = 4/35 ⇒ 1/y+1/x = 4/35 ⇒ 1/x+1/y = 4/35.

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

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