# HCF and LCM Quiz Set 016

### 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.

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 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer