# HCF and LCM Quiz Set 004

### Question 1

The sum of LCM and HCF of two numbers is 420. If LCM is 83 times the HCF, then the product of the two numbers is?

A

2075.

B

2077.

C

2076.

D

2078.

Soln.
Ans: a

Let L be the LCM, and H the HCF. Then H + L = 420, and L = 83H. Solving these for H, we get H = \$420/{83 + 1}\$ = 5, and L = 415. The product of the two numbers is equal to the product of the lcm and hcf = 5 × 415 = 2075.

### Question 2

The HCF of two numbers is 41. The factors of their LCM are 41, 29 and 13. Which is the greater of the two numbers?

A

1189.

B

2378.

C

594.

D

3567.

Soln.
Ans: a

The numbers are 41 × 29 = 1189, and 41 × 13 = 533. The greater of them is 1189.

### Question 3

What is the LCM of 57, 24 and 81?

A

12312.

B

24624.

C

6156.

D

36936.

Soln.
Ans: a

The required LCM = 12312.

### Question 4

Which is the least number which must be added to 7347 so that it becomes divisible by 21, 75 and 98?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

The LCM of 21, 75 and 98 = 7350. The lcm when divided by either of these numbers leaves the remainder 0. The minimum number to be added is 7350 - 7347 = 3.

### Question 5

What is the HCF of (8 × 7), (7 × 16) and (16 × 8)?

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 8, 7 and 16 is 112. So the required HCF = \${8 × 7 × 16}/112\$ = 8. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3. 