LCM of 5 and 6

Find the Least Common Multiple (LCM) of 5 and 6. The LCM is the smallest number that both 5 and 6 divide evenly.

Answer: LCM(5, 6) = 30

Step-by-Step Solution

Step 1 List the Multiples of 5

To find the LCM of 5 and 6, we first list the multiples of each number.

Multiples of 5 are: 5 × 1, 5 × 2, 5 × 3, ...

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...

Step 2 List the Multiples of 6

Now we list the multiples of 6:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...

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 30.

LCM(5, 6) = 30

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

5 = 5

6 = 2 × 3

Take each prime factor with the highest power:

LCM = 2 × 3 × 5 = 30

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(5, 6) = 1

LCM = (5 × 6) ÷ 1 = 30 ÷ 1 = 30

Step 6 Final Answer

LCM(5, 6) = 30