# HCF and LCM Quiz Set 010

### Question 1

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 2

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 3

What is the LCM of \${6/17}\$, \${4/5}\$ and \$2{1/8}\$?

A

204.

B

205.

C

206.

D

207.

Soln.
Ans: a

The LCM of numerators 6, 4 and 17 is 204. The HCF of denominators 17, 5 and 8 is 1. So the required LCM of the given fractions is 204/1 = 204.

### Question 4

The LCM and HCF of two numbers 68 and 98 are in the ratio?

A

1666.

B

\${3333/2}\$.

C

1667.

D

\${3335/2}\$.

Soln.
Ans: a

The LCM of 68 and 98 is 3332, and their HCF is 2. The ratio is: 1666.

### Question 5

The sum of LCM and HCF of two numbers is 188 and LCM is 93 times the HCF. If one of the two numbers is 186, then the other number is?

A

2.

B

4.

C

3.

D

5.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 188, and L = 93H. Solving these for H, we get H = \$188/{93 + 1}\$ = 2, and L = 186. The product of the two numbers is equal to the product of the lcm and hcf = 2 × 186 = 372. The other number is 372/186 = 2.