LCD: 4 fractions w/ denomimators 3a, 24a, 7b, 25b

[algebraiseasy]

I am adding four fractions with the following denominators: 3a,24a,7b and 25b.
My choices are a. 235,200ab , b. 235,200 a^2 b^2 c. 210ab d. None of these
I think I can multiply the coefficients and have 12,600 and variables ab and have a LCD as 12,600ab. Does that sound right?

 

[Loren]

Re: LCD

You are after the "least" common denominator. If the denominators were 12, 18, 9 and 6, you would get 11,664 if you just multiplied them together. That is a "common" denominator, but not the "least" common denominator. The least common denominator can be found this way.

12 = 2[sup:16awad6l]2[/sup:16awad6l]*3
18 = 2*3[sup:16awad6l]2[/sup:16awad6l]
9 = 3[sup:16awad6l]2[/sup:16awad6l]
6 = 2*3

LCD = 2[sup:16awad6l]2[/sup:16awad6l]*3[sup:16awad6l]2[/sup:16awad6l] = 36.

To get that we take each base and attach to that base the largest exponent appearing in any of the factorizations, and multiply those together.

 

[algebraiseasy]

Re: LCD

Like this?
3=3
24= 2^3*2^2
7=7
25=5^2

so 3*2^3*7*5^2= 4200
In my problem it would be 4200ab, correct?

 

[Loren]

Re: LCD

That's what I get.