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 - 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

Answer : C

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 - Which of the following fractions is the largest?

A - 78

B - 1316

C - 3140

D - 6380

Answer : A

Explanation

L.C.M of 8, 16, 40 and 80 = 80
78 = 7080; 1316 = 6580; 3140 = 6280
Since 7080 > 6380 > 6580 > 6280
78 > 6380 > 1316 > 3140
S0, 78 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

Answer : C

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 L.C.M of the two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10 then their difference is?

A - 15

B - 40

C - 10

D - 70

Answer : D

Explanation

Let the numbers be z and (100 - z). Then, z (100 - z) = 5 x 495
= z2 - 100z + 2475 = 0
(z - 55) (z - 45) = 0
z = 55 or z = 45 
 Therefore the numbers are 45 and 55. Required difference is (55 - 45) = 10

Q 5 - The H.C.F and L.C.M of two numbers are 11 and 385 respectively. If one number lies between 75 and 125, then the number is?

A - 88

B - 99

C - 110

D - 77

Answer : D

Explanation

Product of numbers = 11 x 385. 
 let the numbers be 11a and 11b. then 11a x 11b = (4235) = ab = 35
Now co-primes with product 35 are (1, 35) (5, 7).
So the numbers are (11 x 1, 11 x 35) and (11 x 5, 11 x 7).
Since one number lies between 75 and 125 the suitable pair is (55, 77).
Required number = 77.

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 - The G.C.D. of 0.93, 0.60 and 0.75 is:

A - 0.03

B - 0.06

C - 0.09

D - 0.12

Answer : A

Explanation

Given numbers are 0.93, 0.60 and 0.75.   H.C.F. of 93, 60 & 75 is 3.
 H.C.F. of given numbers = 0.03

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 - If the H.C.F of two numbers and their difference is 12 find the numbers.

A - 66, 78

B - 70, 82

C - 94, 106

D - 84, 96

Answer : D

Explanation

The difference of requisite numbers must be 12 and one must be divisible by 12 .
Hence, the required numbers are 84 and 96

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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