# HCF and LCM Quiz Set 008

### Question 1

Three cyclists are cycling in a circular track. They, respectively, take 3, 11 and 18 minutes to complete the circle once. After how many minutes will they all again meet at a single point?

A

198 minutes.

B

396 minutes.

C

99 minutes.

D

199 minutes.

Soln.
Ans: a

The answer lies in finding the LCM of their times. The LCM of 3, 11 and 18 = 198.

### Question 2

The HCF of two numbers is 2. The factors of their LCM are 2, 7 and 13. Which is the greater of the two numbers?

A

26.

B

52.

C

13.

D

78.

Soln.
Ans: a

The numbers are 2 × 7 = 14, and 2 × 13 = 26. The greater of them is 26.

### Question 3

The sum of LCM and HCF of two numbers is 200. If LCM is 99 times the HCF, then the product of the two numbers is?

A

396.

B

398.

C

397.

D

399.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 200, and L = 99H. Solving these for H, we get H = \$200/{99 + 1}\$ = 2, and L = 198. The product of the two numbers is equal to the product of the lcm and hcf = 2 × 198 = 396.

### Question 4

What is the HCF of \$1{1/14}\$, \${5/7}\$ and \${3/4}\$?

A

\${1/28}\$.

B

\${1/14}\$.

C

\${3/28}\$.

D

\${1/7}\$.

Soln.
Ans: a

The HCF of numerators 15, 5 and 3 is 1. The LCM of denominators 14, 7 and 4 is 28. So the required HCF of the given fractions is 1/28 = \${1/28}\$.

### Question 5

Three lights are flashing at regular intervals. They, respectively, flash after 12, 24 and 36 seconds. How many times do they together flash in 1080 seconds?

A

16 times.

B

17 times.

C

15 times.

D

18 times.

Soln.
Ans: a

They will together flash after the LCM of their times. The LCM of 12, 24 and 36 = 72. So they will flash 1 + \$1080/72\$ = 16 times. 