# HCF and LCM Quiz Set 003

### Question 1

Two numbers are in the ratio 4 : 1. If their HCF and LCM are 12 and 48, which of these is the smaller number?

A

12.

B

24.

C

48.

D

6.

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 12.

### Question 2

Two numbers are in the ratio 4 : 1. If their HCF and LCM are 17 and 68, which of these is the smaller number?

A

17.

B

34.

C

68.

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 17.

### Question 3

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 4

The sum of LCM and HCF of two numbers is 112 and LCM is 13 times the HCF. If one of the two numbers is 104, then the other number is?

A

8.

B

10.

C

9.

D

11.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 112, and L = 13H. Solving these for H, we get H = \$112/{13 + 1}\$ = 8, and L = 104. The product of the two numbers is equal to the product of the lcm and hcf = 8 × 104 = 832. The other number is 832/104 = 8.

### Question 5

Which is the second smallest number, which, when divided by 18 and 90, leaves the remainder 2?

A

182.

B

92.

C

272.

D

88.

Soln.
Ans: a

The LCM of 18 and 90 = 90. All the numbers that leave remainder 2 upon being divided by either of the given two numbers are of the form 90k + 2. When k = 1, we get the smallest number, and k = 2 gives the next required number = 182. 