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 - Find the L.C.M of 72, 108, and 2100.

A - 37500

B - 37000

C - 37800

D - 37850

Answer : C

Explanation

72 = 23 x 32
108 = 22 x 33
2100 = 22 x 52 x 3 x7
Therefore L.C.M = 2 3 x 33 x 52 = 37800

Q 2 - H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 x 3 5 x 52 x 72?

A - 23 x 3 5 x 52 x 72

B - 22 x 3 5 x 72

C - 22 x 5 x 72

D - 25 x 5 2 x 72

Answer : B

Explanation

3240 = 23 x 32 x 5; 3600 = 24 x 32 52
H.C.F = 36 = 22 x 32.
Since H.C.F is the product of the lowest powers of common factors so the the third number must have 22 x 32 as its factor
Since L.C.M is the product of highest powers of common prime factors so the third number must have 35 x 72 as its factor
Therefore third number = 22 x 35 x 72

Q 3 - Let the least number of six digit, which when divided by 4,6,10 and 15, leaves in each case the same remainder of 2. The sum of the digits N is?

A - 5

B - 323

C - 4

D - 623

Answer : A

Explanation

Least number of 6 digits  is 100000. L.C.M of 4,6,10 and15 = 60
On dividing 100000 by 60, the remainder obtained is 40.
Therefore Least number of 6 digits divisible by 4,6,10, and 15 = 100000 + (60 - 40) = 100020.
Therefore N = (100020 + 2) = 100022.
Sum of digits in N = (1 + 2 + 2) = 5.

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 - 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 - Find the H.C.F. of 1296 and 2400

A - 96

B - 48

C - 24

D - 12

Answer : B

Explanation

1296=24x34 and 2400=25x3x52
HCF=24x3=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 - If the sum of two numbers is 216 and H.C.F is 27. Find the numbers:

A - 54, 162

B - 108, 108

C - 27, 189

D - none of these

Answer : C

Explanation

let the numbers be 27 a and 27 b.
Then, 27 a +27 b= 216  ⇒ a+b = 216/27 = 8
co-primes with sum 8 are (1,7 ) and (3,5)
So, the numbers are (27*1, 27*7) or (27*3, 27*5)
i.e (27 and 189) or (81 and 135).
Out of the given numbers , the right choice  is 27, 189.

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

Answer : D

Explanation

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


aptitude_hcf_lcm.htm

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