Problems on LCM & HCF Mcqs - Set 7

1)   Which of the following fractions is the largest?

a. 7/8
b. 13/16
c. 31/40
d. 63/80
Answer  Explanation 

ANSWER: 7/8

Explanation:
L.C.M of 8, 16, 40 and 80 = 80.

7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.


2)   The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is___________?

a. 276
b. 299
c. 322
d. 345
Answer  Explanation 

ANSWER: 322

Explanation:
Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322.


3)   The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?

a. 24
b. 48
c. 56
d. 60
Answer  Explanation 

ANSWER: 60

Explanation:
H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.


4)   Product of two co-prime numbers is 117. Their L.C.M should be__________?

a. 1
b. 117
c. equal to their H.C.F
d. Cannot be calculated
Answer  Explanation 

ANSWER: 117

Explanation:
H.C.F of co-prime numbers is 1.

So, L.C.M = 117/1 = 117.


5)   If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to___________?

a. 55/601
b. 601/55
c. 11/120
d. 120/11
Answer  Explanation 

ANSWER: 11/120

Explanation:
Let the numbers be a and b.

Then, a + b = 55 and ab = 5 * 120 = 600.
Required sum = 1/a + 1/b = (a + b)/ab = 55/600 = 11/120.


6)   The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is__________?

a. 10
b. 46
c. 70
d. 90
Answer  Explanation 

ANSWER: 10

Explanation:
Let the numbers be x and (100 – x).

Then, x(100 – x) = 5 * 495
x2 – 100x + 2475 = 0
(x – 55)(x – 45) = 0
x = 55 or 45
The numbers are 45 and 55.
Required difference = 55 – 45 = 10.


7)   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  Explanation 

ANSWER: 308

Explanation:
Other number = (11 * 7700)/275 = 308.


8)   The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is____________?

a. 12
b. 48
c. 84
d. 108
Answer  Explanation 

ANSWER: 84

Explanation:
Let the numbers be x and 4x. Then, x * 4x = 84 * 21 x2 = (84 * 21)/4 = x = 21.

Hence, larger number = 4x = 84.


9)   Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:

a. 40
b. 80
c. 120
d. 200
Answer  Explanation 

ANSWER: 40

Explanation:
Let the numbers be 3x, 4x and 5x.

Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.
The numbers are (3 * 40), (4 * 40) and (5 * 40).
Hence, required H.C.F = 40.


10)   The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is__________?

a. 28
b. 32
c. 40
d. 64
Answer  Explanation 

ANSWER: 40

Explanation:
Let the numbers be 2x and 3x.

Then, their L.C.M = 6x. So, 6x = 48 or x = 8.
The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.