What is the lcm of 4 and 10

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what is the lcm of 4 and 10

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LectureNotes said what is the lcm of 4 and 10

Answer: To find the Least Common Multiple (LCM) of 4 and 10, follow these steps:

1. Factorize Both Numbers

First, determine the prime factorizations of the numbers:

  • The prime factorization of 4 is (2^2).
  • The prime factorization of 10 is (2 \times 5).

2. Identify the Highest Powers of All Prime Factors

Include each prime number raised to the highest power that appears in these factorizations:

  • For the prime factor 2: the highest power that appears is (2^2) (from 4).
  • For the prime factor 5: the highest power is (5^1) (from 10).

3. Calculate the LCM

Multiply these together to find the LCM:

\text{LCM} = 2^2 \times 5^1 = 4 \times 5 = 20

Conclusion

Therefore, the LCM of 4 and 10 is 20.

Using the prime factorization method ensures accuracy, as it covers all necessary multiples. This result can be verified by listing out the multiples and finding the smallest common one:

  • Multiples of 4: 4, 8, 12, 16, 20, 24,…
  • Multiples of 10: 10, 20, 30,…

The smallest common multiple is clearly 20.

Therefore, the least common multiple of 4 and 10 is indeed 20.