# HCF and LCM Quiz Set 005

### Question 1

Find the least possible number that can be divided by 33, 96 as well as 27?

A

9504.

B

19008.

C

4752.

D

28512.

Soln.
Ans: a

The required number is LCM = 9504.

### Question 2

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 3

Three cyclists are cycling in a circular track. They, respectively, take 2, 9 and 18 minutes to complete the circle once. After how many minutes will they all again meet at a single point?

A

18 minutes.

B

36 minutes.

C

9 minutes.

D

19 minutes.

Soln.
Ans: a

The answer lies in finding the LCM of their times. The LCM of 2, 9 and 18 = 18.

### Question 4

The LCM and HCF of two numbers 68 and 98 are in the ratio?

A

1666.

B

\${3333/2}\$.

C

1667.

D

\${3335/2}\$.

Soln.
Ans: a

The LCM of 68 and 98 is 3332, and their HCF is 2. The ratio is: 1666.

### 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.