# HCF and LCM Quiz Set 001

### Question 1

What is the HCF of \${7/15}\$, \$1{7/12}\$ and 3?

A

\${1/60}\$.

B

\${1/30}\$.

C

\${1/20}\$.

D

\${1/15}\$.

Soln.
Ans: a

The HCF of numerators 7, 19 and 3 is 1. The LCM of denominators 15, 12 and 1 is 60. So the required HCF of the given fractions is 1/60 = \${1/60}\$.

### Question 2

Find the largest number that divides each of the numbers 24, 90 and 112 and leaves the same remainder?

A

22.

B

24.

C

23.

D

25.

Soln.
Ans: a

The pair-wise differences are (24 and 90) = 66, (90 and 112) = 22, (112 and 24) = 88. The required number is HCF of 66, 22 and 88 = 22.

### Question 3

The product of LCM and HCF of two numbers is 450? If one of the numbers is 10, what is the other?

A

45.

B

47.

C

46.

D

48.

Soln.
Ans: a

Product of two numbers is equal to the product of their LCM and HCF. So the other number is \$450/10\$ = 45.

### Question 4

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 5

Which is the largest number that divides 30 by leaving a remainder 7, and also divides 31 by leaving a remainder 8?

A

23.

B

24.

C

22.

D

25.

Soln.
Ans: a

The required number is the HCF of 30 - 7 = 23 and 31 - 8 = 23. HCF of 23 and 23 is 23.