Question

The LCM of two or more prime numbers is equal to their product.
A. True
B. False

Answer 1

Hint:Here we use the definition of prime numbers that they have only two factors, 1 and the number itself. Assume two prime numbers as two different variables and find their LCM using prime factorization of both the numbers.

Complete step-by-step answer:
LCM of two numbers is the least common multiple between the two numbers. We write prime factorization of two numbers and calculate the LCM by multiplying the highest degree of prime numbers that are common in the prime factorization.
* Prime numbers are the numbers that are only divided by 1 and the number itself. Example 2,3, 5, 11 etc.
* Prime factorization is a process of writing a number in terms of product of its prime factors.
Let us assume two prime numbers \[a\] and \[b\].
Then using the definition of prime numbers we can write the prime factorization of the two numbers.
\[a = a \times 1\] and \[b = b \times 1\]
Now we know LCM of two numbers is the least common multiple of the two numbers.
LCM of the numbers \[a\]and \[b\] will be the product of prime factors. We have to cover each factor in such a way that there is no repetition of factors.
LCM \[ = 1 \times a \times b\]
Therefore, LCM of two numbers \[a,b = a \times b\]
Since the numbers \[a\] and \[b\] are prime numbers, we can say the LCM of two prime numbers is their product.
Hence, the statement in the question is TRUE.

So, the correct answer is “Option A”.

Note:Students many times get confused between HCF and LCM of two numbers and they write 1 as the LCM as they think the least common term between prime numbers is 1. This is the wrong approach. LCM is the number that is divided by both the numbers so it will have factors from both the numbers. HCF is the highest common factor which is the highest common factor that divides both the numbers.