What is the lcm of 6 and 7

General
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what is the lcm of 6 and 7

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What is the LCM of 6 and 7?

Answer: The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Let’s find the LCM of 6 and 7 step-by-step:

1. Prime Factorization

First, find the prime factors of each number.

  • The prime factors of 6 are:
    6 = 2 \times 3
  • The prime factors of 7 are:
    7 = 7 \text{ (since 7 is a prime number)}

2. Identify the Highest Powers of Each Prime

List all the prime numbers found in either factorization, and choose the highest power of each prime number present.

  • Prime numbers: 2, 3, 7
  • Highest powers for each prime:
    • 2^1 (from 6)
    • 3^1 (from 6)
    • 7^1 (from 7)

3. Calculate the LCM

To find the LCM, multiply the highest powers of each prime number together.

\text{LCM} = 2^1 \times 3^1 \times 7^1

Calculate step-by-step:

2^1 = 2
3^1 = 3
7^1 = 7

Now, multiply them together:

LCM = 2 \times 3 \times 7
2 \times 3 = 6
6 \times 7 = 42

Conclusion

Therefore, the LCM of 6 and 7 is:

\boxed{42}