GCD and LCM using Recursion Multiple choice Questions and Answers (MCQs)

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GCD and LCM using Recursion Multiple choice Questions and Answers (MCQs)

Question 11 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
If gcd (a, b) is defined by the expression, d=a*p + b*q where d, p, q are positive integers and a, b is both not zero, then what is the expression called?
A
Bezout's Identity
B
Multiplicative Identity
C
Sum of Product
D
Product of Sum
Question 11 Explanation: 
If gcd (a, b) is defined by the expression, d=a*p + b*q where d, p, q are positive integers and a, b is both not zero, then the expression is called Bezout's Identity and p, q can be calculated by extended form of Euclidean algorithm.

Question 12 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Is gcd an associative function.
A
True
B
False
Question 12 Explanation: 
The gcd function is an associative function as gcd (a, gcd (b, c)) = gcd (gcd (a, b), c).

Question 13 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Which is the correct term of the given relation, gcd (a, b) * lcm (a, b) =?
A
|a*b|
B
a + b
C
a - b
D
a / b
Question 13 Explanation: 
The gcd is closely related to lcm as gcd (a, b) * lcm (a, b) = |a*b|.

Question 14 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Who gave the expression for the probability and expected value of gcd?
A
James E. Nymann
B
Riemann
C
Thomae
D
Euler
Question 14 Explanation: 
In the year 1972, James E. Nymann showed some result to show the probability and expected value of gcd.

Question 15 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
What is the computational complexity of Binary GCD algorithm where a and b are integers?
A
O (log a + log b)2)
B
O (log (a + b))
C
O (log ab)
D
O (log a-b)
Question 15 Explanation: 
From the Binary GCD algorithm, it is found that the computational complexity is O (log a + log b)2) as the total number of steps in the execution is at most the total sum of number of bits of a and b.

There are 15 questions to complete.