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3. The L.C.M of the first three even numbers is:

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To determine the Least Common Multiple (LCM) of the first three even numbers, let's follow these steps:

1. Identify the first three even numbers:
The first three even numbers are: 2, 4, and 6.

2. Calculate the LCM of the first two numbers:
- LCM of 2 and 4:
- The prime factorization of 2 is [tex]\(2\)[/tex].
- The prime factorization of 4 is [tex]\(2^2\)[/tex].
- The LCM will contain each prime factor the greatest number of times it occurs in any of the factorizations listed:
- LCM(2, 4) = [tex]\(2^2\)[/tex] = 4.

3. Use the result to find the LCM with the next number:
- Now, we need to determine the LCM of 4 and 6:
- The prime factorization of 4 is [tex]\(2^2\)[/tex].
- The prime factorization of 6 is [tex]\(2 \times 3\)[/tex].
- The LCM will contain each prime factor the greatest number of times it occurs in any of the factorizations listed:
- LCM(4, 6) = [tex]\(2^2 \times 3\)[/tex] = 12.

Therefore, the LCM of the first three even numbers (2, 4, and 6) is 12.
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