least common multiple of 3 and 20

Understand the Problem

The question is asking to find the least common multiple (LCM) of the numbers 3 and 20. To solve it, we need to identify the smallest number that is a multiple of both 3 and 20.

Answer

$60$

Steps to Solve

List the multiples of each number

First, let's start by listing the multiples of both 3 and 20.

For 3: The multiples are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
For 20: The multiples are 20, 40, 60, 80, 100, ...

Identify the common multiples

Next, we look for the multiples that appear in both lists:

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The multiples of 20 are: 20, 40, 60, 80, 100, ...

It looks like there are no common multiples until we reach higher numbers.

Find the smallest common multiple

Now we can find the smallest common multiple.

To do this mathematically, we can also use the formula for LCM:

$$ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} $$

Calculate the GCD

First, we need to find the greatest common divisor (GCD) of 3 and 20. Since 3 is a prime number and does not divide 20, we have:

$$ \text{GCD}(3, 20) = 1 $$

Apply the LCM formula

Now, substitute the values for the LCM:

$$ \text{LCM}(3, 20) = \frac{|3 \times 20|}{\text{GCD}(3, 20)} = \frac{60}{1} = 60 $$

Final Result

The least common multiple of 3 and 20 is 60.

The least common multiple of 3 and 20 is $60$.

More Information

The LCM is useful in various applications such as adding fractions with different denominators or solving problems involving periodic events. The method shown can also be applied to larger sets of numbers.

Tips

A common mistake is to confuse the LCM with the GCD. Remember, LCM is the least common multiple, while GCD is the greatest common divisor.
Another mistake can be forgetting to list enough multiples. Always ensure you check enough multiples, or use the formula directly to find the LCM.

Thank you for voting!