Find the least common multiple of the expressions:

1. 2m^{2}n; 3mn^{3}; 9n^{2}p

2. 5x^{3} + 15x^{2}; x^{2} – 6x + 9; 2x^{2} – 6x

Guest Mar 2, 2015

#5**+10 **

For the second one, we have

2. 5x^{3} + 15x^{2}; x^{2} – 6x + 9; 2x^{2} – 6x

Factor each

5x^2(x + 3), (x -3)^2, 2x(x -3)

And the LCM is

10x^2(x + 3)(x -3)^2 = {you could expand this...if you want}

10x^2 (x ^2 - 9) ( x- 3) =

10x^2 (x^3 - 3x^2 - 9x + 27) =

10x^5 - 30x^4 - 90x^3 + 270x^2

CPhill
Mar 3, 2015

#4**+5 **

Sorry, my first answer was garbage and I have whited it.

I must have had a brain aneuryism, or a chronic case of CDD at the very least.

2m^{2}n; 3mn^{3}; 9n^{2}p

2m^{2}n; 3mn^{3}; 3^{2}n^{2}p

The lowest common multiple for the 2'a is 2

The lowest common multiple for the 3's is 3^2=9.

the lowest common multple for the m pronumeral is m^2

the lowest common multple for the n pronumeral is n^3

the lowest common multiple for the p pronumeral is p

Put it all together and you get

$$LCM=18m^2n^3p$$

Melody
Mar 3, 2015

#5**+10 **

Best Answer

For the second one, we have

2. 5x^{3} + 15x^{2}; x^{2} – 6x + 9; 2x^{2} – 6x

Factor each

5x^2(x + 3), (x -3)^2, 2x(x -3)

And the LCM is

10x^2(x + 3)(x -3)^2 = {you could expand this...if you want}

10x^2 (x ^2 - 9) ( x- 3) =

10x^2 (x^3 - 3x^2 - 9x + 27) =

10x^5 - 30x^4 - 90x^3 + 270x^2

CPhill
Mar 3, 2015