RRB NTPC - L.C.M and H.C.F : Aptitude Test

1.

The L.C.M of two prime numbers x and y (x>y) is 203, the value of 2y-x 

   A.) -14
   B.) -15
   C.) 14
   D.) 15

Answer: Option 'B'

-15

2.

The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

   A.) 267
   B.) 318
   C.) 308
   D.) 279

Answer: Option 'C'

Other number = (11 x 7700/275) = 308.

3.

Find the highest common factor of 36 and 84.

   A.) 4
   B.) 6
   C.) 12
   D.) 18

Answer: Option 'C'

36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.

4.

The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

   A.) 1
   B.) 2
   C.) 3
   D.) 4

Answer: Option 'B'

Let the two numbers be 13a and 13b respectively.
Then, 13a x 13b = 2028
=>ab = 2028 / (13 x 13) = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs.

5.

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

   A.) 111
   B.) 101
   C.) 107
   D.) 185

Answer: Option 'A'

Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107 => ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Therefore, Greater number = 111.

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