Design and Analysis of Algorithms MCQs | Page - 1

 least common multiple is also known as lcm or lowest common multiple.

 coprime numbers have gcd 1. while lcm of coprime numbers is the product of those two coprime numbers.

 in terms of venn diagram, the lcm is given by the union of two sets. so a u b gives the lcm. while a ꓵ b gives the gcd.

 in terms of venn diagram, the lcm is given by the union of two sets. so a u b gives the lcm. so product of all the terms is 180.

 since the lcm function is commutative, so lcm (a, b) = lcm (b, a).

 coprime numbers have gcd 1

 since lcm function follows associativity, hence lcm (a, lcm (b, c) is equal to lcm (lcm (a, b), c).

 the lcm function is an associative function as lcm (a, lcm (b, c) is equal to lcm (lcm (a, b), c).

 since the lcm function follows absorption laws so lcm (a, gcd (a, b)) equal to a.

 the most efficient way of calculating the lcm of a given number is using euclid’s algorithm which computes the lcm in much lesser time compared to other algorithms.