Question

Find the LCM of the following numbers in which one number is the factor of the other. $9,45$
What do you observe in the results obtained?

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. 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 of these numbers.

Complete step-by-step answer:
Find the prime factors for the given two numbers.
Prime factorization is well defined as the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are expressed 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 a $1$ factor.
 Here we will find the product of prime factors one by one for both $9,45$ the given numbers.
$
  9 = 3 \times 3 \\
  45 = 3 \times 3 \times 5 \;
 $
LCM can be expressed as the product of highest power of each factor involved among both the numbers.
Therefore, the LCM of the given two numbers $9$and $45$is $3 \times 3 \times 5 = 45$
Hence, we can observe that the smallest number out of two given terms and its multiple gives the larger number. We can also conclude that the LCM (least common multiple) of the two given numbers is the larger number.
So, the correct answer is “45”.

Note: One should be very clear with the concept of HCF and LCM and the prime numbers. HCF is expressed as the highest or greatest common multiple whereas the LCM is expressed as the least common multiple or least common divisor in two or more given numbers Also, remember that we get the prime factorization of any composite number. Be good in multiples to get the correct factors for the given terms.