# HCF and LCM Quiz Set 019

### Question 1

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.

### Question 2

Which is the smallest number which when divided by 11, 11 or 16 leaves 6, 6, 11 as the respective remainders?

A

171.

B

172.

C

170.

D

173.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 5. The LCM of 11, 11 and 16 = 176. So the required number is 176 - 5 = 171.

### Question 3

Which is the largest number that divides 36 by leaving a remainder 3, and also divides 96 by leaving a remainder 8?

A

11.

B

12.

C

10.

D

13.

Soln.
Ans: a

The required number is the HCF of 36 - 3 = 33 and 96 - 8 = 88. HCF of 33 and 88 is 11.

### Question 4

Find the largest number that divides each of the numbers 51, 85 and 21 and leaves the same remainder?

A

2.

B

4.

C

3.

D

5.

Soln.
Ans: a

The pair-wise differences are (51 and 85) = 34, (85 and 21) = 64, (21 and 51) = 30. The required number is HCF of 34, 64 and 30 = 2.

### Question 5

Which is the least number which must be added to 2098 so that it becomes divisible by 15, 50 and 84?

A

2.

B

3.

C

1.

D

4.

Soln.
Ans: a

The LCM of 15, 50 and 84 = 2100. The lcm when divided by either of these numbers leaves the remainder 0. The minimum number to be added is 2100 - 2098 = 2.