HCF and LCM Quiz Set 011

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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.


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This Blog Post/Article "HCF and LCM Quiz Set 011" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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