Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
in Sets, Relations and Functions by (51.8k points)
closed by

Let * be a binary operation on N given by a * b = 1 cm of a and b. Find the value of 20 * 16. Is * (i) commutative, (ii) associative?

1 Answer

+1 vote
by (20.7k points)
selected by
Best answer

We know that a * b = LCM of a and b

So 20 * 16 = LCM of 20 and 16 = 80


Consider a and b ∈ N

So LCM of a and b = LCM of b and a

Here, a * b = b * a Ɐ a and b ∈ N

Therefore, * is commutative.


(a * b) * c = LCM of a and b * c


= LCM of {(LCM of a and b) and C} = LCM of {LCM of a, b and c}

We get

= LCM of (a and [LCM of b and c]) = a * (LCM of b and c)


= a * (b * c)

We can write it as

a * (b * c) = (a * b) * c Ɐ a, b ∈ c ∈ N.

Therefore, * is associative.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.