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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 - 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?

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 - The L.C.M of 22,54, 108, 135 and 198 is?

Answer : A

Explanation

L.C.M = 2 x 3 x 3 x 3 x 11 x 2 x 5 = 5940

Q 3 - The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is?

Answer : A

Explanation

Let the numbers be 33a and 33b. then 33a + 33b = 528
a + b = 16.
Now, co-primes with product 16 are (1,15) (3,13) (5,11) and (7,9)
So, the required numbers are (33 x 1, 33 x 15) (33 x 3, 33 x 13) (33 x 5, 33 x 11) (33 x 7, 33 x 9)
the number of such pairs is 4.

Q 4 - The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of the number is?

Answer : A

Explanation

Let the numbers be 2z, and 3z. then their L.C.M = 6z 
 So, 6z = 48 or z = 8.
Therefore the numbers are 16 and 24
Hence the required sum = 40.

Q 5 - Find the greatest number that will divide 43, 91, and 183 so as to leave the same remainder in each case.

Answer : C

Explanation

Required number = H.C.F of (91 - 43), (183 - 12) and (183 - 43) = H.C.F of 48, 92, and 140 = 4

Q 6 - Find the H.C.F. of 2/3, 2/5 and 2/7

Answer : B

Explanation

H.C.F. of given fractions =  (H.C.F.of denominators)/(L.C.M.of numerators)=2/105
(  H.C.F.of numerators    = 2  L.C.M.of denominators =105)

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

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 ratio of two numbers is 2:3. Having their L.C.M as 150, numbers are :

Answer : C

Explanation

Let the numbers be  2x and 3x . Then, their L.C.M is 6x.
6x =  150    ⇒ x=  25
So, the numbers are 50 and 75.

Q 9 - The H.C.F of three numbers is 12 and they are in the ratio of 1:2:3, find the numbers.

Answer : C

Explanation

Let the numbers be a, 2a , 3a . Then , their H.C.F is a.
∴  a =12  and hence , the numbers  are 12, 24, 36.

Q 10 - What is the greatest length possible of a scale that can be used to measure exactly 7 m, 3 m 85 cm, 12 m 95 cm, is:

Answer : C

Explanation

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

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