Hcf And Lcm Of Numbers MCQ


17 Questions MCQ Test Additional Documents & Tests for CLAT | Hcf And Lcm Of Numbers MCQ


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Attempt Hcf And Lcm Of Numbers MCQ | 17 questions in 15 minutes | Mock test for CLAT preparation | Free important questions MCQ to study Additional Documents & Tests for CLAT for CLAT Exam | Download free PDF with solutions
QUESTION: 1

Test the divisibility of the following numbers by 8
(i) 9364                        
(ii) 2138
(iii) 36792                     
(iv) 901674
(v) 136976                    
(vi) 1580184

Solution:
QUESTION: 2

Test the divisibility of the following numbers by 11
(i) 3443                        
(ii) 13728
(iii) 11366                     
(iv) 137269
(v) 153109                    
(vi) 8790322

Solution:
QUESTION: 3

289/391 when reduced to the lowest terms is

Solution:
QUESTION: 4

Find the greatest number which divides 134 and the 167 leaving 2 as remainder

Solution:
QUESTION: 5

The HCF of two co-primes is

Solution:
QUESTION: 6

If a, b are two co-primes, then their LCM is

Solution:
QUESTION: 7

The product of two number is 2160 and their HCF is 12. The LCM of these numbers is

Solution:
QUESTION: 8

Three bells toll together at intervals 9, 12, 15 minutes. They start tolling together. At what interval of time will they toll together again

Solution:

Three bells toll at intervals - 9min , 12 min and 15min.
So, if they start tolling together, they will ring together at LCM ( 9,12,15)
So, We have to find LCM of 9 , 12 and 15.
9 = 3×3
12 = 2×2×3
15 = 3×5 
LCM (9, 12,15) = 3×3×2×2×5 = 180
So , the LCM of 9 , 12 and 15 is 180. The bells will toll together after 180 minutes or 3 hours.
Bells will toll together after 180 minutes or 3 hours.

QUESTION: 9

Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are

Solution:

Let the required numbers be x, 2x, 3x.  
Then, their H.C.F =x. so, x= 12
Therefore, The numbers are 12, 24, 36

QUESTION: 10

The sum of two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above condition is

Solution:

Let the required numbers be 33a and 33b. 
Then 33a +33b= 528 ⇒ a+b = 16.
Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).
Therefore, 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

QUESTION: 11

The product of two numbers is 4107. If the HCF of these numbers is 37 then the greatest number is

Solution:
QUESTION: 12

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

Solution:
QUESTION: 13

Three numbers are in the ratio of 3 : 4 : 5 and their LCM is 2400. Their HCF is

Solution:

Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.

QUESTION: 14

The HCF and LCM of two numbers are 21 and 84 respectively. If the ratio of the two numbers be 1 : 4, the larger of the two  numbers is

Solution:
QUESTION: 15

If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case, then sum of the digits in N is

Solution:

N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

  = H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

QUESTION: 16

The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54. Is

Solution:
QUESTION: 17

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes how many times do they toll together

Solution:
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