Question

What is the LCM of 2, 3 and 9?

Answer 1

Hint: LCM or least common multiple is the simplest method to find out the smallest common multiples between two or more than two numbers. Generally, the common multiple is a number which is a multiple of two or more than two numbers.

Complete step by step solution:
We have 2, 3 and 9.
We can find the LCM by using the factorization method.
We know that the factors of 2 are 2 and 1 only.
The factors of 3 are 1 and 3 only.
The factors of 9 are 3 and 3.
\[ \Rightarrow 2 = 1 \times 2\]
\[ \Rightarrow 3 = 1 \times 3\]
\[ \Rightarrow 9 = 1 \times 3 \times 3\]
Then the LCM of 2, 3 and 9 are \[ \Rightarrow 2 \times 3 \times 3\].
That is \[ 18\]
Hence the LCM of 2, 3 and 9 is 18.
So, the correct answer is “18”.

Note: We know that if we have a LCM of prime numbers, then their LCM is their product itself. That is for example LCM of 2 and 11 is given by \[2 \times 11 = 22\]. We also have HCF or the highest common factor. That is the largest common factor of all the given numbers is known as the Highest common factor of the number. The HCF of 2, 3 and 9 is 3 (from above factors).