What is the least common multiple of 12 and 19?

1 Answer
Sep 24, 2016

This is quite a nice question, with an interesting concept....
19 is a prime factor which means it only has factors of 1 and 19.

While 12 is a composite number, it has no common factor with 19. (apart from 1).
Therefore the lowest common multiple will be the product of the numbers. #19 xx12 = 228#

This can further be shown by finding the prime factors:

#color(white)(xxxxx)12 = 2xx2xx3#
#color(white)(xxxxx)19 =color(white)(xxxxxx.xx)19#

#LCM = color(white)(xxx)2xx2xx3xx19 = 228#

The LCM must have all of the factors of 12 as well as all of the factors of 19.