Aptitude - Problems on H.C.F and L.C.M

Exercise :: Problems on H.C.F and L.C.M - General Questions

16. 

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. 279
B. 283
C. 308
D. 318

Answer: Option C

Explanation:

Other number = 11 x 7700 = 308.
275

17. 

What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?

A. 196
B. 630
C. 1260
D. 2520

Answer: Option B

Explanation:

 L.C.M. of 12, 18, 21 30                 2 | 12  -  18  -  21  -  30
                                         ----------------------------
   = 2 x 3 x 2 x 3 x 7 x 5 = 1260.       3 |  6  -   9  -  21  -  15
                                         ----------------------------
   Required number = (1260  2)            |  2  -   3  -   7  -   5

                   = 630.

18. 

The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:

A. 12
B. 16
C. 24
D. 48

Answer: Option D

Explanation:

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.

So, the numbers 12 and 16.

L.C.M. of 12 and 16 = 48.


19. 

The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

A. 1008
B. 1015
C. 1022
D. 1032

Answer: Option B

Explanation:

Required number = (L.C.M. of 12,16, 18, 21, 28) + 7

   = 1008 + 7

   = 1015


20. 

252 can be expressed as a product of primes as:

A. 2 x 2 x 3 x 3 x 7
B. 2 x 2 x 2 x 3 x 7
C. 3 x 3 x 3 x 3 x 7
D. 2 x 3 x 3 x 3 x 7

Answer: Option A

Explanation:

Clearly, 252 = 2 x 2 x 3 x 3 x 7.




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