how can you use the prime factorization of two numbers to find their common multiples?

Answer 1

im not sure i forgot but i think if u keep getting all the prime factors of both the numbers until ur down to all prime numbers then u multiply them all and ull get the common multiple

Answer 2

Brittana M has given you the correct methodology for finding the LEAST common multiple (LCM) of two integers, and this might be what you're asking for. In fact, there are an infinite number of common multiples of two numbers. If you have any common multiple, you can multiply it by 2, 3, 4, ... to create additional common multiples.

That being said, the smallest of the common multiples, is the one that has every prime factor that is in either of the two numbers, and includes that prime factor as many times as either of the two numbers (but NO MORE times than it appears in one of the two numbers). And this is the method provided by Brittana M.

Additional idea: You might need to find the least common multiple of MORE than two numbers. For example, if you are adding 3 or more fractions, and you need to find a denominator that you can convert them all to. In that case, use Brittana M's method, but just check ALL of the denominators and make sure your LCM includes all the prime factors in ALL of the denominators, and that it includes each one exactly as many times as the most times it appears in any of the denominators.

Answer 3

do the prime factorization
take the highest power of each number and add them together


EX.

prime fac. of 36.. 2x2x3x3.... which is 2 squared times 3 squared
prime fac. of 90.. 3x3x2x5... which is 3 squared times 2 times 5

the highest power of 2 is 2squared
the highest power of 3 is 3squared
highest power of 5 is 5

2squared times 3 squared times 5
180