LCM of 36 and 48

Find the Least Common Multiple (LCM) of 36 and 48. The LCM is the smallest number that both 36 and 48 divide evenly.

Answer: LCM(36, 48) = 144

Step-by-Step Solution

Step 1 List the Multiples of 36

To find the LCM of 36 and 48, we first list the multiples of each number.

Multiples of 36 are: 36 × 1, 36 × 2, 36 × 3, ...

Multiples of 36: 36, 72, 108, 144, 180, 216, ...

Step 2 List the Multiples of 48

Now we list the multiples of 48:

Multiples of 48: 48, 96, 144, 192, 240, ...

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 144.

LCM(36, 48) = 144

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

36 = 2^2 × 3^2

48 = 2^4 × 3

Take each prime factor with the highest power:

LCM = 2^4 × 3^2 = 144

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(36, 48) = 12

LCM = (36 × 48) ÷ 12 = 1728 ÷ 12 = 144

Step 6 Final Answer

LCM(36, 48) = 144