The least common multiple of 2 and any other number will be(1 point) Responses either even or odd, it just depends on the other number. either even or odd, it just depends on the other number. even because all multiples of 2 are even. even because all multiples of 2 are even. even because 2 is the smallest possible multiple. even because 2 is the smallest possible multiple. odd because all numbers can be divided by 1. odd because all numbers can be divided by 1.
even because all multiples of 2 are even.
The least common multiple (LCM) of 2 and any other number will always be even because all multiples of 2 are even. Therefore, among the options given, the correct response is "even because all multiples of 2 are even."
The least common multiple (LCM) of 2 and any other number can be determined by finding the smallest multiple that is divisible by both 2 and the other number. In this case, since 2 is a prime number, all of its multiples will only be divisible by 2 and 1. Therefore, the LCM of 2 and any other number will always be even.
To find the LCM of 2 and another number, you can use a few different methods. One common method is to list the multiples of both numbers and find the smallest multiple that they have in common. Another method is to use prime factorization. By expressing both numbers as a product of their prime factors, you can find the highest power of each prime factor that appears in either number, and multiply them together to get the LCM.
For example, let's say we are trying to find the LCM of 2 and 6.
Method 1: Listing Multiples
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
From the list, we can see that the smallest multiple that both 2 and 6 have in common is 6. Therefore, LCM(2, 6) = 6.
Method 2: Prime Factorization
2 = 2^1 (2 is already a prime number)
6 = 2^1 * 3^1 (prime factorization of 6)
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^1 * 3^1 = 6.
Therefore, LCM(2, 6) = 6.
In both methods, we find that the LCM of 2 and 6 is 6, which is even. This pattern holds for any other number when finding the LCM with 2, as 2 is always even.