# HCF and LCM Quiz Set 011

### Question 1

Which is the smallest number which when divided by 15, 12 or 14 leaves 12, 9, 11 as the respective remainders?

A

417.

B

418.

C

416.

D

419.

Soln.
Ans: a

By inspection, the difference between the numbers and their respective remainders is same = 3. The LCM of 15, 12 and 14 = 420. So the required number is 420 - 3 = 417.

### Question 2

The LCM and HCF of two numbers 36 and 86 are in the ratio?

A

774.

B

\${1549/2}\$.

C

775.

D

\${1551/2}\$.

Soln.
Ans: a

The LCM of 36 and 86 is 1548, and their HCF is 2. The ratio is: 774.

### Question 3

What is the HCF of (3 × 7), (7 × 18) and (18 × 3)?

A

3.

B

6.

C

1.

D

9.

Soln.
Ans: a

The required HCF is product of the three numbers divided by their LCM. The LCM of 3, 7 and 18 is 126. So the required HCF = \${3 × 7 × 18}/126\$ = 3. Please note that LCM(n1, n2, n3) × HCF(n1 × n2, n2 × n3, n3 × n1) = n1 × n2 × n3.

### Question 4

Which is the second smallest number, which, when divided by 12 and 55, leaves the remainder 5?

A

1325.

B

665.

C

1985.

D

655.

Soln.
Ans: a

The LCM of 12 and 55 = 660. All the numbers that leave remainder 5 upon being divided by either of the given two numbers are of the form 660k + 5. When k = 1, we get the smallest number, and k = 2 gives the next required number = 1325.

### Question 5

Three cyclists are cycling in a circular track. They, respectively, take 4, 7 and 22 minutes to complete the circle once. After how many minutes will they all again meet at a single point?

A

308 minutes.

B

616 minutes.

C

154 minutes.

D

309 minutes.

Soln.
Ans: a

The answer lies in finding the LCM of their times. The LCM of 4, 7 and 22 = 308. 