# HCF and LCM Quiz Set 017

### Question 1

What is the LCM of 51, 66 and 36?

A

6732.

B

13464.

C

3366.

D

20196.

Soln.
Ans: a

The required LCM = 6732.

### Question 2

What is the LCM of 48, 24 and 72?

A

144.

B

288.

C

72.

D

432.

Soln.
Ans: a

The required LCM = 144.

### Question 3

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 4

The sum of LCM and HCF of two numbers is 372 and LCM is 92 times the HCF. If one of the two numbers is 368, then the other number is?

A

4.

B

6.

C

5.

D

7.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 372, and L = 92H. Solving these for H, we get H = \$372/{92 + 1}\$ = 4, and L = 368. The product of the two numbers is equal to the product of the lcm and hcf = 4 × 368 = 1472. The other number is 1472/368 = 4.

### Question 5

What is the HCF of 36, 48 and 27?

A

3.

B

6.

C

1.

D

9.

Soln.
Ans: a

The required HCF = 3. 