HCF and LCM Quiz Set 016

Advertisement


Your Score
Correct Answers:
Wrong Answers:
Unattempted:

Question 1

Which is the smallest number, which, when divided by 24 and 85, leaves the remainder 8?

 A

2048.

 B

2050.

 C

2047.

 D

2051.

Soln.
Ans: a

The LCM of 24 and 85 = 2040, is the smallest number, which, when divided by either of them leaves the remainder 0. Now adding, 2040 + 8 = 2048 is the required number.


Question 2

Find the largest number that divides each of the numbers 21, 75 and 105 and leaves the same remainder?

 A

6.

 B

8.

 C

7.

 D

9.

Soln.
Ans: a

The pair-wise differences are (21 and 75) = 54, (75 and 105) = 30, (105 and 21) = 84. The required number is HCF of 54, 30 and 84 = 6.


Question 3

Find the largest number that divides each of the numbers 45, 35 and 21 and leaves the same remainder?

 A

2.

 B

4.

 C

3.

 D

5.

Soln.
Ans: a

The pair-wise differences are (45 and 35) = 10, (35 and 21) = 14, (21 and 45) = 24. The required number is HCF of 10, 14 and 24 = 2.


Question 4

The sum of LCM and HCF of two numbers is 420. If LCM is 83 times the HCF, then the product of the two numbers is?

 A

2075.

 B

2077.

 C

2076.

 D

2078.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 420, and L = 83H. Solving these for H, we get H = $420/{83 + 1}$ = 5, and L = 415. The product of the two numbers is equal to the product of the lcm and hcf = 5 × 415 = 2075.


Question 5

What is the HCF of (3 × 7), (7 × 18) and (18 × 3)?

 A

3.

 B

6.

 C

1.

 D

9.

Soln.
Ans: a

The required HCF is product of the three numbers divided by their LCM. The LCM of 3, 7 and 18 is 126. So the required HCF = ${3 × 7 × 18}/126$ = 3. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3.


buy aptitude video tutorials


Creative Commons License
This Blog Post/Article "HCF and LCM Quiz Set 016" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


Advertisement