# 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

-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

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

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

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