# HCF and LCM Quiz Set 020

### Question 1

Three cyclists are cycling in a circular track. They, respectively, take 6, 7 and 19 minutes to complete the circle once. After how many minutes will they all again meet at a single point?

A

798 minutes.

B

1596 minutes.

C

399 minutes.

D

799 minutes.

Soln.
Ans: a

The answer lies in finding the LCM of their times. The LCM of 6, 7 and 19 = 798.

### Question 2

The sum of LCM and HCF of two numbers is 112 and LCM is 13 times the HCF. If one of the two numbers is 104, then the other number is?

A

8.

B

10.

C

9.

D

11.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 112, and L = 13H. Solving these for H, we get H = \$112/{13 + 1}\$ = 8, and L = 104. The product of the two numbers is equal to the product of the lcm and hcf = 8 × 104 = 832. The other number is 832/104 = 8.

### Question 3

Which is the second smallest number, which, when divided by 12 and 55, leaves the remainder 5?

A

1325.

B

665.

C

1985.

D

655.

Soln.
Ans: a

The LCM of 12 and 55 = 660. All the numbers that leave remainder 5 upon being divided by either of the given two numbers are of the form 660k + 5. When k = 1, we get the smallest number, and k = 2 gives the next required number = 1325.

### Question 4

What is the LCM of 51, 66 and 36?

A

6732.

B

13464.

C

3366.

D

20196.

Soln.
Ans: a

The required LCM = 6732.

### Question 5

The HCF of two numbers is 19. The factors of their LCM are 19, 7 and 31. Which is the greater of the two numbers?

A

589.

B

1178.

C

294.

D

1767.

Soln.
Ans: a

The numbers are 19 × 7 = 133, and 19 × 31 = 589. The greater of them is 589.