What is the least common multiple (LCM) of 4 and 5?

What is the least common multiple (LCM) of 4 and 5?

• A. 9
• B. 10
• C. 20
• D. 30

Answer: (C)

To determine the least common multiple (LCM) of 4 and 5, we need to identify the smallest number that is a multiple of both numbers. First, we can list the multiples of each number: - The multiples of 4 are: 4, 8, 12, 16, 20, 24, ... - The multiples of 5 are: 5, 10, 15, 20, 25, ... Next, we look for the smallest number that appears in both lists. In this case, the number 20 is present in both lists, making it the least common multiple. To verify, we can also calculate the LCM by using the formula based on the greatest common divisor (GCD). The GCD of 4 and 5 is 1 since they have no common factors. The LCM can be calculated as: \[ \text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)} \] Plugging the values in: \[ \text{LCM}(4, 5) = \frac{4 \times 5}{1} = 20 \

To determine the least common multiple (LCM) of 4 and 5, we need to identify the smallest number that is a multiple of both numbers.

First, we can list the multiples of each number:

• The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...

• The multiples of 5 are: 5, 10, 15, 20, 25, ...

Next, we look for the smallest number that appears in both lists. In this case, the number 20 is present in both lists, making it the least common multiple.

To verify, we can also calculate the LCM by using the formula based on the greatest common divisor (GCD). The GCD of 4 and 5 is 1 since they have no common factors. The LCM can be calculated as:

[

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

]

Plugging the values in:

[

\text{LCM}(4, 5) = \frac{4 \times 5}{1} = 20

\