# HCF and LCM Quiz Set 018

### Question 1

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 2

What is the HCF of \$1{5/8}\$, \$1{3/5}\$ and \${5/17}\$?

A

\${1/680}\$.

B

\${1/340}\$.

C

\${3/680}\$.

D

\${1/170}\$.

Soln.
Ans: a

The HCF of numerators 13, 8 and 5 is 1. The LCM of denominators 8, 5 and 17 is 680. So the required HCF of the given fractions is 1/680 = \${1/680}\$.

### Question 3

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 4

Which is the smallest number, which, when divided by 21 and 85, leaves the remainder 8?

A

1793.

B

1795.

C

1792.

D

1796.

Soln.
Ans: a

The LCM of 21 and 85 = 1785, is the smallest number, which, when divided by either of them leaves the remainder 0. Now adding, 1785 + 8 = 1793 is the required number.

### Question 5

Two numbers are in the ratio 4 : 1. If their HCF and LCM are 15 and 60, which of these is the smaller number?

A

15.

B

30.

C

60.

D

7.

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 15. 