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

## 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.