Find the least common multiple of 2 and 12.(1 point)
Responses
2
24
12
36
The least common multiple of 2 and 12 is 12.
To find the least common multiple (LCM) of 2 and 12, we can list the multiples of each number and find the smallest number that appears in both lists.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...
Multiples of 12: 12, 24, 36, 48, 60, ...
The least common multiple (LCM) is 12, which is the smallest number that appears in both lists.
Therefore, the correct answer is 12.
To find the least common multiple (LCM) of two numbers, you can start by finding their prime factorization. Let's do that for 2 and 12.
2 can only be divided evenly by itself and 1, so its prime factorization is simply 2.
12 can be divided evenly by 2 and 3. Therefore, its prime factorization is 2 * 2 * 3.
Now, to find the LCM, we take the highest power of each prime factor present in either number. In this case, we have 2^2 and 3^1.
The LCM is then the product of these prime factors raised to their highest powers: 2^2 * 3^1 = 4 * 3 = 12.
Therefore, the least common multiple of 2 and 12 is 12.