# HCF and LCM Quiz Set 012

### Question 1

Which is the least number which must be added to 23933 so that it becomes divisible by 18, 95 and 84?

A

7.

B

8.

C

6.

D

9.

Soln.
Ans: a

The LCM of 18, 95 and 84 = 23940. The lcm when divided by either of these numbers leaves the remainder 0. The minimum number to be added is 23940 - 23933 = 7.

### Question 2

The sum of LCM and HCF of two numbers is 42. If LCM is 20 times the HCF, then the product of the two numbers is?

A

80.

B

82.

C

81.

D

83.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 42, and L = 20H. Solving these for H, we get H = \$42/{20 + 1}\$ = 2, and L = 40. The product of the two numbers is equal to the product of the lcm and hcf = 2 × 40 = 80.

### Question 3

The sum of LCM and HCF of two numbers is 712. If LCM is 88 times the HCF, then the product of the two numbers is?

A

5632.

B

5634.

C

5633.

D

5635.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 712, and L = 88H. Solving these for H, we get H = \$712/{88 + 1}\$ = 8, and L = 704. The product of the two numbers is equal to the product of the lcm and hcf = 8 × 704 = 5632.

### Question 4

Find the least possible number that can be divided by 42, 30 as well as 117?

A

8190.

B

16380.

C

4095.

D

24570.

Soln.
Ans: a

The required number is LCM = 8190.

### Question 5

What is the HCF of (10 × 12), (12 × 16) and (16 × 10)?

A

8.

B

16.

C

4.

D

24.

Soln.
Ans: a

The required HCF is product of the three numbers divided by their LCM. The LCM of 10, 12 and 16 is 240. So the required HCF = \${10 × 12 × 16}/240\$ = 8. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3.