What is the Equation of 3,5,7 LCM prime factorization method
The correct answer and explanation is:
Correct Answer:
To find the Least Common Multiple (LCM) of 3, 5, and 7 using prime factorization, the equation involves expressing each number as a product of its prime factors, then taking the highest power of each prime factor.
- Prime factors of 3 = 3
- Prime factors of 5 = 5
- Prime factors of 7 = 7
Since all are prime numbers, the LCM is simply the product of these numbers:
LCM(3, 5, 7) = 3 × 5 × 7 = 105
Explanation:
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of them. The prime factorization method involves breaking down each number into its prime factors and then combining these factors to find the LCM.
For the numbers 3, 5, and 7, each is already a prime number, meaning they cannot be factored further into smaller prime numbers. The prime factorization method requires us to list out these prime factors.
To find the LCM, identify all unique prime factors from the given numbers and multiply them together using the highest power of each prime that appears in any of the numbers. Here, 3, 5, and 7 are all distinct primes with a power of 1 in their factorization.
Therefore, the LCM is calculated by multiplying all these prime factors:
3 (from 3), 5 (from 5), and 7 (from 7).
Multiplying them gives 3 × 5 = 15, then 15 × 7 = 105.
This means 105 is the smallest number that can be divided evenly by 3, 5, and 7 without leaving a remainder.
In summary, the LCM using prime factorization for the numbers 3, 5, and 7 is 105, found by multiplying the prime factors since none of the numbers share common prime factors.