# HCF and LCM Quiz Set 002

### Question 1

What is the HCF of 15, 66 and 153?

A

3.

B

6.

C

1.

D

9.

Soln.
Ans: a

The required HCF = 3.

### Question 2

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 3

The sum of LCM and HCF of two numbers is 42. If LCM is 20 times the HCF, then the product of the two numbers is?

A

80.

B

82.

C

81.

D

83.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 42, and L = 20H. Solving these for H, we get H = \$42/{20 + 1}\$ = 2, and L = 40. The product of the two numbers is equal to the product of the lcm and hcf = 2 × 40 = 80.

### Question 4

Which is the largest number that divides 20 by leaving a remainder 5, and also divides 86 by leaving a remainder 11?

A

15.

B

16.

C

14.

D

17.

Soln.
Ans: a

The required number is the HCF of 20 - 5 = 15 and 86 - 11 = 75. HCF of 15 and 75 is 15.

### Question 5

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

A

4.

B

8.

C

16.

D

2.

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 4.