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

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

• A. 10
• B. 15
• C. 20
• D. 25

Answer: (C)

To determine the least common multiple (LCM) of 4 and 5, you want to find the smallest multiple that both numbers share. Start with the multiples of each number. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The multiples of 5 are 5, 10, 15, 20, 25, etc. Looking through both lists, the first number that appears in both sets is 20. Thus, the LCM of 4 and 5 is indeed 20. Calculating the LCM can also be done using the prime factorization method, where you take the highest powers of all prime factors involved. For number 4, the prime factorization is \(2^2\), and for number 5, it is \(5^1\). The LCM will take the highest powers, which results in: \[ LCM = 2^2 \times 5^1 = 4 \times 5 = 20. \] This confirms that the least common multiple of 4 and 5 is 20, making the choice correct.

To determine the least common multiple (LCM) of 4 and 5, you want to find the smallest multiple that both numbers share.

Start with the multiples of each number. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The multiples of 5 are 5, 10, 15, 20, 25, etc.

Looking through both lists, the first number that appears in both sets is 20. Thus, the LCM of 4 and 5 is indeed 20.

Calculating the LCM can also be done using the prime factorization method, where you take the highest powers of all prime factors involved. For number 4, the prime factorization is (2^2), and for number 5, it is (5^1). The LCM will take the highest powers, which results in:

[

LCM = 2^2 \times 5^1 = 4 \times 5 = 20.

]

This confirms that the least common multiple of 4 and 5 is 20, making the choice correct.