Question

How do you find the LCM of $ 7 $ and $ 9? $

Answer 1

Hint: LCM (Least common Multiple) can be defined as the least or the smallest number with which the given numbers are exactly divisible. In other words, LCM is also known as the least common divisor. Here first of all we will find the prime factors of the given two numbers and then LCM.

Complete step-by-step answer:
First of all the prime factors of the given two numbers.
Prime factorization is defined as the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are defined as the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor. Here we will find the product of prime factors one by one for both the given numbers.
 $
  7 = 1 \times 7 \\
  9 = 3 \times 3 \;
  $
LCM can be expressed as the product of highest power of each factor involved in the numbers. Since in the factor of the given two numbers there are no common factors.
Therefore, the LCM of the given two numbers $ 7 $ and $ 9 $ is $ 3 \times 3 \times 7 = 63 $
So, the correct answer is “63”.

Note: To solve these types of sums, one should be very clear with the concept of HCF and LCM and the prime numbers. HCF is defined as the highest or greatest common multiple whereas the LCM is defined as the least common multiple or least common divisor in two or more given numbers. Prime numbers are the numbers which are greater than $ 1 $ and also which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor. Factors can be defined as the number $ 1 $ and the number itself. Also, remember that we get the prime factorization of any given composite number.