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 - Reduce 128352238368 to its lowest terms.

A - 713

B - 34

C - 513

D - 913

Answer : A

Explanation

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 - The least number, which when divided by 48, 60, 72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is?

A - 11115

B - 15110

C - 15120

D - 15210

Answer : B

Explanation

Here (48 - 38) = 10, (60 - 50) = 10, (72 - 62) = 10, (108 - 98) = 10 & (140 - 130) = 10
Therefore Required number = (L.C.M  of 48,60,72,108,140) - 10 = 15120 - 10 =15110.

Q 4 - The H.C.F and L.C.M of the two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger number of the twi is?

A - 84

B - 48

C - 58

D - 80

Answer : A

Explanation

Let the number be z and 4z. Then z x 4z = 84 x 21 
 = z2 = 84 x 214 = z = 21
Hence larger number is 4z = 4 x 21 = 84

Q 5 - Let N be the greatest number that will divide 1305, 4665 and 6905 leaving the same remainder in each case. then the sum of the digits in N is?

A - 5

B - 4

C - 6

D - 8

Answer : B

Explanation

N = H.C.F of (4665 - 1305), (6905 - 4665), (6905 - 1305)
= H.C.F of 3360, 2240 and 5600 = 1120.
Sum of digits in N = (1 + 1 + 2 + 0) = 4.

Q 6 - The least square number which is divisible by 12, 14 and 18 is:

A - 1764

B - 1600

C - 1444

D - 1296

Answer : A

Explanation

The least number divisible by12, 14 and 18 is their L.C.M. which is 252.
Now 252=2*2*3*3*7
To make it a perfect square, it must be multiplied by 7
2*2*3*3*7*7=1764

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 - H.C.F and L.C.M of two 3-digit numbers are 29 and 4147 respectively. What is the sum of the numbers?

A - 666

B - 669

C - 696

D - 966

Answer : C

Explanation

Let the numbers be 29a and 29 b , where a and b  are co-primes.
Then, 29 a * 29 b + 29*147 ⇒ ab + (29*4147)/(29*29)= 143
co-primes with product 143 are 11  and 13.
∴ numbers are (29*11,   29* 13) i.e ,  319, 377
Their sum = (319+377)= 696

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

A - 6, 12, 18

B - 10, 20 ,30

C - 12, 24, 36

D - 24, 48, 72

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 - If the capacity of two pots is 120 liters and 56 liters. Find the container capacity which can exactly measure the contents of the two pots, is :

A - 7500 cc

B - 7850 cc

C - 8000 cc

D - 9500 cc

Answer : C

Explanation

Required capacity = H.C.F of 120 L and 56 L.= 8 L = 8000cc 


aptitude_hcf_lcm.htm

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