Question

Find the Least Common Multiple or L.C.M of 2 and 5?

Answer 1

Hint: We must identify the least common multiple (LCM) of 2, 5 from the given question. We will use the prime factorization method to find the LCM. We will write each of the supplied numbers as the product of its prime components. If a prime factor is going to reoccur or repeat, we will write it in exponential form. Then, we'll multiply all of the prime components together with their highest exponent and get the final result.

Complete step-by-step solution:
We have to find the LCM of 2 and 5
We should know the definition of the L.C.M. In arithmetic and number theory, the smallest positive integer that is divisible by each of the given numbers is called the least common multiple. The specified integers can't be zero. To find the LCM of two or more numbers, we can use one of the two methods.
We'll utilize prime factorization to solve this problem.
We will write the provided numbers as the product of their prime components in the prime factorization method. The LCM will now be the product of the prime factors and their highest exponent if any are present.
We have given 2 and 5 which are already prime numbers so there is no further factor of them.
\[ \Rightarrow 2 = {2^1}\]
\[ \Rightarrow 5 = {5^1}\]
We can clearly observe that the maximum power of the prime factors 2 and 5 is 1.
So, we will multiply 2 and 5 to get the L.C.M
\[ \Rightarrow L.C.M = 2 \times 5\]
\[ \Rightarrow L.C.M = 10\]
Hence, the L.CM. of 2 and 5 is 10.\[ \Rightarrow L.C.M = 10\].

Note: We can also remember a short way to find the LCM of two prime numbers which is the LCM of two prime numbers is their product. This is because they cannot be factored. This is applied for two or more than two prime numbers as well.