L.C.M of two co – prime numbers is their
(A). sum
(B). difference
(C). product
(D). quotient

Question

L.C.M of two co – prime numbers is their(A). sum(B). difference(C). product(D). quotient

Vedantu Content Team · Accepted Answer

Hint: Use definition of co – prime and then find a point which leads us to the least common multiple of the numbers. Find the relation between the least common multiple the co – primes and the co – prime itself. That will become our final result.

Complete step-by-step answer:

Numbers:
A number is a mathematical object or thought which is used to count, measure and represent. Types of numbers possible are natural numbers, whole numbers, integers, rational numbers, irrational.
Prime numbers:
A prime number is a natural number greater than 1 that is not a product of 2 smaller natural numbers. It will have only 2 factors: 1 and itself.
Composite numbers:
A composite number is a natural number greater than that is possible to break into product of 2 smaller natural numbers. It is also said the natural number which is not prime is composite.
Co – prime:
If two numbers have no common factor then they are said to co – primes. It also follows the analogy of prime numbers. So the pair following that there doesn’t exist any common factor between then they are co – primes.
Least common multiple:
In arithmetic and number theory, the least common multiple of two integers a, b is the smallest positive integer that is divisible by both a and b.
In our question we need the least common multiple of 2 co – primes. As they do not have any common factors. So, a number which is divisible by both must at least contain them both.
\[\Rightarrow \] LCM (co - primes) = product of those co – primes.
Hence option C is the correct answer.

Note: It is important to note co –primes have analogy of prime numbers. The idea of finding that no common factors between given numbers implies that the numbers’ factors cannot be combined and their product cannot be diminished to find least common multiple. So the only least multiple which is divisible by both of the numbers will be the product of them. This point is very important to understand.