# HCF and LCM Quiz Set 013

### Question 1

The product of LCM and HCF of two numbers is 3720? If one of the numbers is 62, what is the other?

A

60.

B

62.

C

61.

D

63.

Soln.
Ans: a

Product of two numbers is equal to the product of their LCM and HCF. So the other number is \$3720/62\$ = 60.

### Question 2

What is the HCF of \${6/19}\$, \${13/14}\$ and \$2{2/5}\$?

A

\${1/1330}\$.

B

\${1/665}\$.

C

\${3/1330}\$.

D

\${2/665}\$.

Soln.
Ans: a

The HCF of numerators 6, 13 and 12 is 1. The LCM of denominators 19, 14 and 5 is 1330. So the required HCF of the given fractions is 1/1330 = \${1/1330}\$.

### Question 3

Three cyclists are cycling in a circular track. They, respectively, take 5, 13 and 22 minutes to complete the circle once. After how many minutes will they all again meet at a single point?

A

1430 minutes.

B

2860 minutes.

C

715 minutes.

D

1431 minutes.

Soln.
Ans: a

The answer lies in finding the LCM of their times. The LCM of 5, 13 and 22 = 1430.

### Question 4

What is the HCF of (19 × 7), (7 × 6) and (6 × 19)?

A

1.

B

2.

C

0.

D

3.

Soln.
Ans: a

The required HCF is product of the three numbers divided by their LCM. The LCM of 19, 7 and 6 is 798. So the required HCF = \${19 × 7 × 6}/798\$ = 1. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3.

### 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.