any common multiples of these three numbers would be a multiple of all three of the numbers. so multiply them
Hey guys, not sure how to state this problem.
I am given the numbers 4,6, and 7. I am then told to find the common numbers of these 3 numbers from 1 to 400? How do I go about it besides listing all the multiples of 4, 6, and 7, and then finding the similar numbers? Thanks for any suggestions!
Mr_fantastic,
Do you mind explaining why you chose 2^2 * 3 * 7 as the common factors? For example, why did you leave out the other 2? Or why not 2 * 3 * 7 instead of 2^2 * ... ?
I am just trying to figure out a methodical method to solve these types of problems and it seems your answer fits this, but just help me understand it.
Thanks!
adding on to what mr. fantastic had said
when factorized
he canceled off one of the 2's because in the factorized form u should be able to form each of the original numbers with the least amount of numbers used, in order to get your lowest common multiple
like for you can form a 4 u can also form a 6 and also a 7 therefore this will give u, ur lowest common multiple which is 84
Because and so therefore is not a factor of .
This method is a methodical way to find the lcm of a set of numbers - break them down into their prime factors and form the number you get by taking the highest indices of those primes that you find in those numbers, and multiply it together.
This is the sort of thing you learn formally in an elementary number theory class at Uni level - it's straightforward to understand but rather trickier to prove.