LCM of 9 and 12

Find the Least Common Multiple (LCM) of 9 and 12. The LCM is the smallest number that both 9 and 12 divide evenly.

Answer: LCM(9, 12) = 36

Step-by-Step Solution

Step 1 List the Multiples of 9

To find the LCM of 9 and 12, we first list the multiples of each number.

Multiples of 9 are: 9 × 1, 9 × 2, 9 × 3, ...

Multiples of 9: 9, 18, 27, 36, 45, 54, ...

Step 2 List the Multiples of 12

Now we list the multiples of 12:

Multiples of 12: 12, 24, 36, 48, 60, ...

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 36.

LCM(9, 12) = 36

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

9 = 3^2

12 = 2^2 × 3

Take each prime factor with the highest power:

LCM = 2^2 × 3^2 = 36

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(9, 12) = 3

LCM = (9 × 12) ÷ 3 = 108 ÷ 3 = 36

Step 6 Final Answer

LCM(9, 12) = 36