Question

Find LCM of \[9\] and \[18\].
A) \[81\]
B) \[28\]
C) \[12\]
D) \[18\]

Answer 1

Hint: We can use the prime factorization method to find the Lowest Common Multiple i.e. LCM in the given question. We shall write the numbers as a product of prime factors and will take the product of all different prime factors to arrive at the answer.

Complete step by step solution:
The LCM of any two numbers is the value that is equally divisible by the two numbers. Least Common Multiple is the full form of LCM. The Least Common Divisor is another name for it (LCD). For example - LCM \[(4,5) = 20\]. Both \[4\] and \[5\] will divide the divisor \[20\]. The point to be noted is that the given integer cannot be \[0\].
Now let us use the prime factorization method to find out the LCM as follows:
We will write the given numbers as product of their prime factors-
\[9 = 3 \times 3\]
\[18 = 3 \times 3 \times 2\]
We can write it in exponential form as follows:
\[9 = {3^2}\]
\[18 = {3^2} \times {2^1}\]
Now we just need to multiply the different prime factors according to their highest exponent to find out the LCM. In the given case, we shall multiply \[{3^2}\] and \[{2^1}\] as highest exponent of \[3\] is \[2\] and of \[2\] is \[1\] between both the given numbers.
\[LCM = {3^2} \times {2^1}\]
\[LCM = 9 \times 2\]
\[LCM = 18\].
Thus, the LCM of \[9\]and \[18\]is \[18\].
Hence, Option (D) \[18\] is the correct answer.

Note:
We can find out the LCM by another method where we can write all the multiples of both the numbers one-by-one and see which common multiple occurs first.
Example- Multiplication table can be constructed as follows:
\[9 \times 1 = 9\]
\[9 \times 2 = 18\]
\[18 \times 1 = 18\]
Since \[18\] occurs first, it will be the LCM.
This method is generally not preferable since we do not know how many multiples we need to write to find out the answer.