LCM of 24 and 36

Find the Least Common Multiple (LCM) of 24 and 36. The LCM is the smallest number that both 24 and 36 divide evenly.

Answer: LCM(24, 36) = 72

Step-by-Step Solution

Step 1 List the Multiples of 24

To find the LCM of 24 and 36, we first list the multiples of each number.

Multiples of 24 are: 24 × 1, 24 × 2, 24 × 3, ...

Multiples of 24: 24, 48, 72, 96, 120, ...

Step 2 List the Multiples of 36

Now we list the multiples of 36:

Multiples of 36: 36, 72, 108, 144, ...

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 72.

LCM(24, 36) = 72

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

24 = 2^3 × 3

36 = 2^2 × 3^2

Take each prime factor with the highest power:

LCM = 2^3 × 3^2 = 72

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(24, 36) = 12

LCM = (24 × 36) ÷ 12 = 864 ÷ 12 = 72

Step 6 Final Answer

LCM(24, 36) = 72