LCM of 20 and 30

Find the Least Common Multiple (LCM) of 20 and 30. The LCM is the smallest number that both 20 and 30 divide evenly.

Answer: LCM(20, 30) = 60

Step-by-Step Solution

Step 1 List the Multiples of 20

To find the LCM of 20 and 30, we first list the multiples of each number.

Multiples of 20 are: 20 × 1, 20 × 2, 20 × 3, ...

Multiples of 20: 20, 40, 60, 80, 100, ...

Step 2 List the Multiples of 30

Now we list the multiples of 30:

Multiples of 30: 30, 60, 90, 120, ...

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 60.

LCM(20, 30) = 60

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

20 = 2^2 × 5

30 = 2 × 3 × 5

Take each prime factor with the highest power:

LCM = 2^2 × 3 × 5 = 60

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(20, 30) = 10

LCM = (20 × 30) ÷ 10 = 600 ÷ 10 = 60

Step 6 Final Answer

LCM(20, 30) = 60