Find the LCM for each set of numbers or monomials.?

Question

1) 14xy,28
2) 17xy, 15x^2z
3) 12am^2,18a^3m
4) -120x^2,150xy
5) 105x^3y^2,165x^2y^4
6) 9r^2t^2,12r^2

Answer 1

The least common multiple has a name that is somewhat misleading, because it is greater than or equal to the largest of the terms. It is called least common multiple becuase it is the smallest term that can be divided by (is a multiple of) the terms in the set. To find the LCM, do the following:
Factor each element of the set into its prime factors
Multiply together each of the prime factors of all the elements, in the hightest power that they occur.
A related concept, with a misleading name also, is the greatest common divisor, or GCD. The GCD is less than or equal to the smallest element of the set. It is the largest term that will divide all members of the set. So your LCMS are ...
1) 28xy
2) 17*15x^2yz
3) 36a^3m^2
4) -600s^2y
5) 5x3x7x31x^3y^4
6) 36r^2t^2