HCF and LCM Quiz Set 004

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.