# HCF and LCM Quiz Set 014

### Question 1

Which is the smallest number which when divided by 15, 17 or 14 leaves 10, 12, 9 as the respective remainders?

A

3565.

B

3566.

C

3564.

D

3567.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 5. The LCM of 15, 17 and 14 = 3570. So the required number is 3570 - 5 = 3565.

### Question 2

The product of LCM and HCF of two numbers is 3360? If one of the numbers is 80, what is the other?

A

42.

B

44.

C

43.

D

45.

Soln.
Ans: a

Product of two numbers is equal to the product of their LCM and HCF. So the other number is \$3360/80\$ = 42.

### Question 3

Two numbers are in the ratio 4 : 1. If their HCF and LCM are 16 and 64, which of these is the smaller number?

A

16.

B

32.

C

64.

D

8.

Soln.
Ans: a

Since the numbers are in an integral ratio, the LCM is equal to the larger number, and HCF is equal to the smaller number. So the smaller is 16.

### Question 4

Which is the second smallest number, which, when divided by 6 and 80, leaves the remainder 6?

A

486.

B

246.

C

726.

D

234.

Soln.
Ans: a

The LCM of 6 and 80 = 240. All the numbers that leave remainder 6 upon being divided by either of the given two numbers are of the form 240k + 6. When k = 1, we get the smallest number, and k = 2 gives the next required number = 486.

### Question 5

The LCM and HCF of two numbers 99 and 15 are in the ratio?

A

165.

B

\${496/3}\$.

C

\${497/3}\$.

D

166.

Soln.
Ans: a

The LCM of 99 and 15 is 495, and their HCF is 3. The ratio is: 165. This Blog Post/Article "HCF and LCM Quiz Set 014" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-02