HCF and LCM Quiz Set 004

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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 HCF of $1{5/8}$, $1{3/5}$ and ${5/17}$?

 A

${1/680}$.

 B

${1/340}$.

 C

${3/680}$.

 D

${1/170}$.

Soln.
Ans: a

The HCF of numerators 13, 8 and 5 is 1. The LCM of denominators 8, 5 and 17 is 680. So the required HCF of the given fractions is 1/680 = ${1/680}$.


Question 3

The HCF of two numbers is 7. The factors of their LCM are 7, 13 and 5. Which is the greater of the two numbers?

 A

91.

 B

182.

 C

45.

 D

273.

Soln.
Ans: a

The numbers are 7 × 13 = 91, and 7 × 5 = 35. The greater of them is 91.


Question 4

Which is the second smallest number, which, when divided by 6 and 80, leaves the remainder 6?

 A

486.

 B

246.

 C

726.

 D

234.

Soln.
Ans: a

The LCM of 6 and 80 = 240. All the numbers that leave remainder 6 upon being divided by either of the given two numbers are of the form 240k + 6. When k = 1, we get the smallest number, and k = 2 gives the next required number = 486.


Question 5

Which is the largest number that divides 30 by leaving a remainder 7, and also divides 31 by leaving a remainder 8?

 A

23.

 B

24.

 C

22.

 D

25.

Soln.
Ans: a

The required number is the HCF of 30 - 7 = 23 and 31 - 8 = 23. HCF of 23 and 23 is 23.


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This Blog Post/Article "HCF and LCM Quiz Set 004" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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