problems on hcf and lcm

Aptitude Data Interpretation Practice Paper Quantitative Railway Reasoning

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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