# HCF and LCM Quiz Set 008

### Question 1

Find the largest number that divides each of the numbers 6, 90 and 70 and leaves the same remainder?

A

4.

B

6.

C

5.

D

7.

Soln.
Ans: a

The pair-wise differences are (6 and 90) = 84, (90 and 70) = 20, (70 and 6) = 64. The required number is HCF of 84, 20 and 64 = 4.

### Question 2

What is the HCF of 42, 114 and 117?

A

3.

B

6.

C

1.

D

9.

Soln.
Ans: a

The required HCF = 3.

### Question 3

What is the HCF of (12 × 17), (17 × 4) and (4 × 12)?

A

4.

B

8.

C

2.

D

12.

Soln.
Ans: a

The required HCF is product of the three numbers divided by their LCM. The LCM of 12, 17 and 4 is 204. So the required HCF = \${12 × 17 × 4}/204\$ = 4. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3.

### Question 4

The LCM and HCF of two numbers 6 and 84 are in the ratio?

A

14.

B

\${85/6}\$.

C

\${43/3}\$.

D

\${29/2}\$.

Soln.
Ans: a

The LCM of 6 and 84 is 84, and their HCF is 6. The ratio is: 14.

### Question 5

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.