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 lowest common multiple of 24, 36 and 40?

A - 120

B - 360

C - 240

D - 480

Answer : B

Explanation

L.C.M = 2 x 2 x 2 x 3 x 3 x 5 = 360

Q 2 - The L.C.M of 22,54, 108, 135 and 198 is?

A - 5940

B - 5420

C - 5400

D - 5900

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?

A - 4

B - 6

C - 8

D - 12

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 - Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. the sum of the three numbers is?

A - 45

B - 85

C - 60

D - 65

Answer : B

Explanation

Since the numbers are co-prime they contain only 1 as the common factor. Also the given two products have the middle number in common.
So, the middle number = H.C.F of 551 and 1073 = 29;
First number = 55129 = 19; Third number = 107329 = 37
required sum = (19 + 29 + 37) = 85.

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 - 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 - Having H.C.F and L.C.M of two numbers as 21 and 4641 respectively. If one of the numbers is in between 200 and 300, then the two numbers are :

A - 273, 363

B - 273, 359

C - 273, 361

D - 273, 357

Answer : D

Explanation

Let the numbers be 21 a and 21 b, where a and b are co-primes.
Then ,21 a* 21 b= (21* 4641)⇒ab= 221.
Two co-primes with product 221 are 13 and 17.
∴ Numbers are (21*13, 21*17) , i.e (273,357)

Q 9 - If ratio of two numbers is 2:3 and the product of their H.C.F and L.C.M is 33750, find the sum of the numbers:

A - 250

B - 325

C - 375

D - 425

Answer : C

Explanation

Let the numbers be 2x and 3x.  Then, H.C.F = x and L.C.M = 6x
∴ 6x*x = 33750  ⇒ x2 = 5625   ⇒ &sqrt;5625= 75
So, the numbers are 150  and 225 . Their sum is 375.

Q 10 - Find the largest fraction among the following:

A - 7/8

B - 13/16

C - 31/40

D - 63/80

Answer : A

Explanation

L.C.M of 8, 16,40 , 80 is 80.
7/8  =  (7/8 *10/10 ) = 70/80  , 13/16 = (13/16*5/5)=  65/80 ,31/40 = (31/40* 2/2 )= 62/80,63/80
Clearly ,70/80 > 65/80 >63/80 >62/80 . Hence, 7/8 is the largest.


aptitude_hcf_lcm.htm

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