# HCF and LCM Quiz Set 018

### Question 1

What is the LCM of 48, 24 and 72?

A

144.

B

288.

C

72.

D

432.

Soln.
Ans: a

The required LCM = 144.

### Question 2

Which is the smallest number, which, when divided by 21 and 75, leaves the remainder 3?

A

528.

B

530.

C

527.

D

531.

Soln.
Ans: a

The LCM of 21 and 75 = 525, is the smallest number, which, when divided by either of them leaves the remainder 0. Now adding, 525 + 3 = 528 is the required number.

### Question 3

The product of LCM and HCF of two numbers is 6300? If one of the numbers is 75, what is the other?

A

84.

B

86.

C

85.

D

87.

Soln.
Ans: a

Product of two numbers is equal to the product of their LCM and HCF. So the other number is \$6300/75\$ = 84.

### Question 4

Which is the smallest number which when divided by 15, 9 or 16 leaves 9, 3, 10 as the respective remainders?

A

714.

B

715.

C

713.

D

716.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 6. The LCM of 15, 9 and 16 = 720. So the required number is 720 - 6 = 714.

### Question 5

What is the HCF of \${6/19}\$, \${13/14}\$ and \$2{2/5}\$?

A

\${1/1330}\$.

B

\${1/665}\$.

C

\${3/1330}\$.

D

\${2/665}\$.

Soln.
Ans: a

The HCF of numerators 6, 13 and 12 is 1. The LCM of denominators 19, 14 and 5 is 1330. So the required HCF of the given fractions is 1/1330 = \${1/1330}\$.