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# How do I find the least common multiple...

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Find the least common multiple of the expressions:

1. 2m2n; 3mn3; 9n2p

2. 5x3 + 15x2; x2 – 6x + 9; 2x2 – 6x

Guest Mar 2, 2015

#5
+92763
+10

For the second one, we have

2. 5x3 + 15x2; x2 – 6x + 9; 2x2 – 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
#2
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Thanks. I guess I did something wrong because I got 18 as my answer, not 54.

Guest Mar 3, 2015
#4
+94114
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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.

2m2n; 3mn3; 9n2p

2m2n; 3mn3; 32n2p

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
+92763
+10

For the second one, we have

2. 5x3 + 15x2; x2 – 6x + 9; 2x2 – 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
#6
+94114
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Thanks Chris :)

Melody  Mar 3, 2015
#7
+5

Thanks guys! Both my answers were corrrect! :)

Guest Mar 3, 2015
#8
+94114
0

That is excellent!

Melody  Mar 3, 2015