# HCF and LCM Quiz Set 019

### Question 1

The sum of LCM and HCF of two numbers is 150 and LCM is 24 times the HCF. If one of the two numbers is 144, then the other number is?

A

6.

B

8.

C

7.

D

9.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 150, and L = 24H. Solving these for H, we get H = \$150/{24 + 1}\$ = 6, and L = 144. The product of the two numbers is equal to the product of the lcm and hcf = 6 × 144 = 864. The other number is 864/144 = 6.

### Question 2

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 3

Find the least possible number that can be divided by 9, 18 as well as 108?

A

108.

B

216.

C

54.

D

324.

Soln.
Ans: a

The required number is LCM = 108.

### Question 4

What is the HCF of \$3{2/5}\$, \$1{2/7}\$ and \$1{1/5}\$?

A

\${1/35}\$.

B

\${2/35}\$.

C

\${3/35}\$.

D

\${4/35}\$.

Soln.
Ans: a

The HCF of numerators 17, 9 and 6 is 1. The LCM of denominators 5, 7 and 5 is 35. So the required HCF of the given fractions is 1/35 = \${1/35}\$.

### Question 5

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. 