The greatest common factor of 2 numbers is the same as the least common multiple of 4 and 6 . Which 2 numbers could they be?

1 Answer

There is an infinite number of solutions. One set of numbers that will work is 24, 36.

Explanation:

The LCM of 4 and 6 is 12. Let's do a prime factorization to see why:

#4=2xx2#

#6=2xx3#

We want the largest groupings of each of the primes, and so that's the two 2s in the 4 and the one 3 in the 6:

#LCM=2xx2xx3=12#

Now we have 12 as the GCF of two numbers, which simply means that we can multiply 12 by two different numbers and so long as those numbers don't share a common factor, it'll work (meaning there is a whole series of solutions to this problem). One straightforward way to work this is to only use primes as the other factor (but note that this ends up being an over simplification - there are other solutions than what my method will come up with):

#12xx2=color(green)24, 12xx3=color(green)36#

#12xx5=color(green)60, 12xx7=color(green)84#

and so on...