find the LCM of (6+5p), (36-25p^2), and (6-5p)
2007-08-20 19:48:32 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
First take the lowest two quantities, and since you know the LCM has to contain each of them, multiply them together. (6+5p)x(6-5p) comes out to be (36-25p^2), so the LCM of the three quanitities happens to be (36 -25p^2).
2007-08-20 19:56:50 · answer #1 · answered by Macho-man 3 · 2⤊ 0⤋
This is the same kind of least common multiple (LCM) you were working with back in elementary school when you were working only with integer prime numbers. However, your stock of primes now also includes all unfactorable polynomials, including factors 6 + 5p and 6 - 5p that are two of the polynomials for which you are finding the LCM. The LCM must therefore include both of these primes.
However, 36 - 25p^2 can be factored as a difference of perfect squares into (6 + 5p) (6 - 5p), both factors of which are already included in the partial LCM from the two primes. No further factors are needed; all three polynomials will divide evenly into (6 + 5p) (6 - 5p) which is the LCM.
2007-08-20 20:02:31 · answer #2 · answered by devilsadvocate1728 6 · 0⤊ 0⤋
LCM of (6-5p), (36-25p^2) and (6-5p)
36-25p^2 = (6-5p)(6+5p)
Hence the LCM = 36-25p^2
2007-08-21 05:19:24 · answer #3 · answered by vr n 2 · 0⤊ 0⤋
LCM means the smallest number evenly divisible by the numbers being considered. 36-25p² factors into 6+5p and 6-5p. So it can be divided by each of them and also by itself. Therefore 36-25p² is the Least Common Multiple
2007-08-20 19:59:12 · answer #4 · answered by chasrmck 6 · 0⤊ 0⤋
(6+5p) , (36-25p^2) , (6-5p)
= (6+5p) , (6+5p)(6-5p) , (6-5p)
LCM is
=(6+5p)(6-5p)
2007-08-21 21:05:24 · answer #5 · answered by billako 6 · 0⤊ 0⤋