Problems on H.C.F and L.C.M - Quantitative Aptitude (MCQ) questions

1)   The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?
- Published on 15 Apr 16

a. 375
b. 2570
c. 2800
d. 3315
e. None of these
Answer  Explanation 

ANSWER: 3315

Explanation:
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. Of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cm. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315


2)   The L.C.M. of two number is 60. The numbers are in the ratio 4 : 5. Find the sum of numbers.
- Published on 12 Apr 16

a. 27
b. 33
c. 38
d. 45
Answer  Explanation 

ANSWER: 27

Explanation:
Let the numbers be 4x and 5x.
Then, their L.C.M. = 20x.
20x = 60 or x = 3.
The numbers are 12 and 15.
Hence, required sum = (12 + 15) = 27.


3)   The L.C.M. Of 2, 2.7 and 0.09 is:
- Published on 07 Apr 16

a. 5.4
b. 0.54
c. 0.054
d. 54
Answer  Explanation 

ANSWER: 54

Explanation:
Given numbers are 2.00, 2.70 and 0.09.
L.C.M. of 200, 270 and 9 is 5400.
L.C.M. Of given numbers = 54.00 = 54


4)   The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?
- Published on 05 Apr 16

a. 375
b. 2570
c. 2800
d. 3315
e. None of these
Answer  Explanation 

ANSWER: 3315

Explanation:
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cms. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315


5)   Find the least number which should be added to 2430 so that the sum is exactly divisible by 5, 4 and 2
- Published on 25 Mar 16

a. 3
b. 10
c. 13
d. 33
Answer  Explanation 

ANSWER: 10

Explanation:
L.C.M of 5, 4, and 2 = 20. On dividing 2430 by 20, the remainder is 10.
Therefore, number to be added = (20 - 10) = 10


6)   The ratio of two numbers is 4 : 5 and their H.C.F is 4. Find their L.C.M.
- Published on 22 Mar 16

a. 96
b. 80
c. 73
d. 48
Answer  Explanation 

ANSWER: 80

Explanation:
Let the numbers be 4x and 5x.

H.C.F = x. So, x=4.
So, the numbers are 16 and 20
L.C.M of 16 and 20 = 80.


7)   A man decides to pave with square tiles his hall which is 4.8 metres long and 5.38 metres wide. Find the largest size of the tile that he could use.
- Published on 06 Jul 15

a. 21 cm
b. 2 cm
c. 269 cm
d. None of these
Answer  Explanation 

ANSWER: 2 cm

Explanation:
The largest size of the tile is H.C.F. of 480 cm and 538 cm is 2 cm.


8)   3 bells beep at an interval of 12, 20, and 35 minutes. If they beep together at 10 a.m., then they will again beep together at:
- Published on 06 Jul 15

a. 12 p.m.
b. 1 p.m.
c. 4 p.m.
d. 5 p.m.
Answer  Explanation 

ANSWER: 5 p.m.

Explanation:
The L.C.M. of 12, 20 and 35 is 420. Hence, all 3 bells beep together after 420 minutes = 7 hours
Hence, the 3 bells will beep together 7 hours after 10 a.m. i.e. at 5 p.m.


9)   The least number which is a multiple of 11 and when divided by 3, 5 and 9 leaves 2 as remainder:
- Published on 06 Jul 15

a. 297
b. 319
c. 407
d. None of these
Answer  Explanation 

ANSWER: 407

Explanation:
The L.C.M. of 3, 5 and 9 is 45.
Hence, the number is of the form (45a + 2).
The least value of ‘a’ for which (45a + 2) is multiple of 11 is 9.
Therefore, the number is 407.


10)   LCM of two numbers is 495. HCF of these numbers is 5. If the sum of the numbers is 100, find out the difference between the two numbers.
- Published on 15 Jun 15

a. 15
b. 12
c. 10
d. 20
Answer  Explanation 

ANSWER: 10

Explanation:
It is given that sum of two numbers is 100. Let the two numbers be x and 100 – x and HCF is 5 and LCM is 495

=> We need to apply the formula: HCF x LCM = Product of two numbers

Which gives x(100 – x) = 495 x 5

Solving the equation we get a quadratic which looks like this:

x2 – 100x + 2475 = 0

=> (x – 55)(x- 45) = 0

Therefore, Two numbers are 55 and 45


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