LCM of 16 and 24

Find the Least Common Multiple (LCM) of 16 and 24. The LCM is the smallest number that both 16 and 24 divide evenly.

Answer: LCM(16, 24) = 48

Step-by-Step Solution

Step 1 List the Multiples of 16

To find the LCM of 16 and 24, we first list the multiples of each number.

Multiples of 16 are: 16 × 1, 16 × 2, 16 × 3, ...

Multiples of 16: 16, 32, 48, 64, 80, ...

Step 2 List the Multiples of 24

Now we list the multiples of 24:

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

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 48.

LCM(16, 24) = 48

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

16 = 2^4

24 = 2^3 × 3

Take each prime factor with the highest power:

LCM = 2^4 × 3 = 48

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(16, 24) = 8

LCM = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

Step 6 Final Answer

LCM(16, 24) = 48