LCM of 18 and 27

Find the Least Common Multiple (LCM) of 18 and 27. The LCM is the smallest number that both 18 and 27 divide evenly.

Answer: LCM(18, 27) = 54

Step-by-Step Solution

Step 1 List the Multiples of 18

To find the LCM of 18 and 27, we first list the multiples of each number.

Multiples of 18 are: 18 × 1, 18 × 2, 18 × 3, ...

Multiples of 18: 18, 36, 54, 72, 90, ...

Step 2 List the Multiples of 27

Now we list the multiples of 27:

Multiples of 27: 27, 54, 81, 108, ...

Step 3 Find the Least Common Multiple

The common multiples are numbers that appear in both lists.

The smallest common multiple is the LCM.

Looking at both lists, the first number that appears in both is 54.

LCM(18, 27) = 54

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

18 = 2 × 3^2

27 = 3^3

Take each prime factor with the highest power:

LCM = 2 × 3^3 = 54

Step 5 Using the GCF Formula

The LCM can be calculated using the GCF with this formula:

LCM(a, b) = (a × b) ÷ GCF(a, b)

GCF(18, 27) = 9

LCM = (18 × 27) ÷ 9 = 486 ÷ 9 = 54

Step 6 Final Answer

LCM(18, 27) = 54