# HCF and LCM Quiz Set 005

### Question 1

What is the LCM of \${10/17}\$, \${7/18}\$ and \$3{2/3}\$?

A

770.

B

771.

C

772.

D

773.

Soln.
Ans: a

The LCM of numerators 10, 7 and 11 is 770. The HCF of denominators 17, 18 and 3 is 1. So the required LCM of the given fractions is 770/1 = 770.

### Question 2

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.

### Question 3

Which is the second smallest number, which, when divided by 15 and 55, leaves the remainder 2?

A

332.

B

167.

C

497.

D

163.

Soln.
Ans: a

The LCM of 15 and 55 = 165. All the numbers that leave remainder 2 upon being divided by either of the given two numbers are of the form 165k + 2. When k = 1, we get the smallest number, and k = 2 gives the next required number = 332.

### Question 4

Which is the largest number that divides 32 by leaving a remainder 2, and also divides 87 by leaving a remainder 12?

A

15.

B

16.

C

14.

D

17.

Soln.
Ans: a

The required number is the HCF of 32 - 2 = 30 and 87 - 12 = 75. HCF of 30 and 75 is 15.

### Question 5

What is the LCM of 42, 72 and 153?

A

8568.

B

17136.

C

4284.

D

25704.

Soln.
Ans: a

The required LCM = 8568.