1) To find the LCM of 5x^2-20 and 3x+6, we first factor each polynomial. 5x^2-20 = 5(x^2-4) = 5(x+2)(x-2), and 3x+6 = 3(x+2). The LCM of these two polynomials is the product of the highest powers of all the factors. The factors are 3, 5, x+2, and x-2. Since the highest power of 3 is 3^1, the highest power of 5 is 5^1, the highest power of x+2 is (x+2)^1, and the highest power of x-2 is (x-2)^1, the LCM is 3*5*(x+2)*(x-2) = 15(x^2-4).
2) To find the LCM of 9c-15 and 21c-35, we first factor each polynomial. 9c-15 = 3(3c-5), and 21c-35 = 7(3c-5). The LCM of these two polynomials is the product of the highest powers of all the factors. The factors are 3 and 7, and 3c-5. Since the highest power of 3 is 3^1, the highest power of 7 is 7^1, and the highest power of 3c-5 is (3c-5)^1, the LCM is 3*7*(3c-5) = 21(3c-5).