The Least Common Multiple (LCM) of two numbers (9 and 18) is the smallest number that is a multiple of both numbers.

In simple words, it is the smallest number that can be divided by both numbers by 9 and 18 without leaving a remainder, that is called a least common multiple of 9 and 18.

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## How to Least Common Multiple of 9 and 18?

To find the LCM (Least Common Multiple) of 9 and 18, you can use the following steps:

List the multiples of each number:

**Multiples of 9**: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …**Multiples of 18**: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …

Find the smallest multiple that is common to both lists:

**The smallest multiple that is common to both lists is 18. Therefore, the LCM of 9 and 18 is 18.**

**Answer:** **Least Common Multiple of 9 and 18 is 18.**

Another way to find the LCM of 9 and 18 is by using the formula:

LCM(9, 18) = (9 x 18) / GCD(9, 18)

where GCD(9, 18) is the Greatest Common Divisor (GCD) of 9 and 18. Using this formula, we can calculate the LCM as follows:

LCM(9, 18) = (9 x 18) / GCD(9, 18) = 162 / 9 = 18

Note that GCD (9,18) = 9

Using prime factorization method

Factorize the numbers into their prime factors 9 = 3^2 18 = 2*3^2

Take the highest power of each prime factor 3^2

Multiply all the prime factors together, it will give the LCM LCM(9, 18) = 36

## Find Least Common Multiple of 9 and 18 with GCF Formula

The formula of Least Common Multiple LCM is LCM(a,b) = ( a × b) / GCF(a,b).

- GCF(9,18) = 9
- LCM(9,18) = ( 9 × 18) / 9
- LCM(9,18) = 162 / 9
- LCM(9,18) = 18

## How to Find Least Common Multiple (LCM) of 9 and 18 with Primes?

By multiplying the greatest exponent prime factors of 9 and 18, the least common multiple may be calculated.

So, to calculate the Least Common Multiple of 9 and 18 you need to calculate the prime factors of 9 and 18.

- Prime Factorization of 9 = 32
- Prime Factorization of 18 = 21 × 32

Now, By multiply highest exponent prime factors of 9 & 18 number. By this you can get the **LCM of 9 and 18**.

- LCM(9,18) = 3
^{2}× 2^{1} - LCM(9,18) = 18

Hence, the least common multiple (LCM) of 9 and 18 is **18**. It can be calculated using different methods like listing multiples, using formula and prime factorization method.