# HCF and LCM Quiz Set 020

### Question 1

Which is the smallest number which when divided by 9, 14 or 16 leaves 3, 8, 10 as the respective remainders?

A

1002.

B

1003.

C

1001.

D

1004.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 6. The LCM of 9, 14 and 16 = 1008. So the required number is 1008 - 6 = 1002.

### Question 2

What is the LCM of 7, \$1{6/13}\$ and \${18/19}\$?

A

2394.

B

2395.

C

2396.

D

2397.

Soln.
Ans: a

The LCM of numerators 7, 19 and 18 is 2394. The HCF of denominators 1, 13 and 19 is 1. So the required LCM of the given fractions is 2394/1 = 2394.

### Question 3

Find the largest number that divides each of the numbers 6, 90 and 70 and leaves the same remainder?

A

4.

B

6.

C

5.

D

7.

Soln.
Ans: a

The pair-wise differences are (6 and 90) = 84, (90 and 70) = 20, (70 and 6) = 64. The required number is HCF of 84, 20 and 64 = 4.

### Question 4

Find the least possible number that can be divided by 42, 90 as well as 126?

A

630.

B

1260.

C

315.

D

1890.

Soln.
Ans: a

The required number is LCM = 630.

### Question 5

Find the least possible number that can be divided by 18, 12 as well as 108?

A

108.

B

216.

C

54.

D

324.

Soln.
Ans: a

The required number is LCM = 108. 