Admin Table of Contents
- 1 How can you tell from the prime factorization of two numbers if their LCM equals the product of the numbers explain your reasoning?
- 2 How do you know when the least common multiple of two numbers is the product of the number?
- 3 How to find the least common multiple of two common primes?
- 4 How do you find the factorization of prime numbers?
- 5 Why do we look at multiples and primes?
How can you tell from the prime factorization of two numbers if their LCM equals the product of the numbers explain your reasoning?
A. The LCM equals the product of the numbers if, and only if, the numbers have no prime factors in common. Because GCD(a, b) – LCM(a, b) = ab, LCM(a, b) = ab, if, and only if, GCD(a, b) = 1, that is, a and have no prime factors in common.
How do you know when the least common multiple of two numbers is the product of the number?
The Least Common Multiple of two numbers is the product of the two numbers only when they are relatively prime.
How do you use prime Factorizations?
To take a prime factorization of a number, start by dividing the number by its lowest prime factor. Write down this factor, and divide the new number by its lowest prime factor (it does not matter if this is the same as the first prime factor). Write this factor down and divide the new number by its lowest factor.
How to find the least common multiple of two common primes?
By matching up the common primes, each common prime factor is used only once. This ensures that 36 is the least common multiple. Step 1. Find the prime factorization of each number.
How do you find the factorization of prime numbers?
Prime Factors Method 1 Find the prime factorization of each number. 2 Write each number as a product of primes, matching primes vertically when possible. 3 Bring down the primes in each column. 4 Multiply the factors to get the LCM.
Does prime factorization work in LCM?
This time the numbers are relatively larger than the previous example. However, don’t fret because as long as you stick to the procedure, the entire solving process for LCM is going to be smooth sailing. That’s the testament to the power of prime factorization.
Why do we look at multiples and primes?
One of the reasons we look at multiples and primes is to use these techniques to find the least common multiple of two numbers. This will be useful when we add and subtract fractions with different denominators. A common multiple of two numbers is a number that is a multiple of both numbers.