10/10/10

Set 1:
1.) The gcd and lcm usually have common multiples or one of the numbers is the divisor of the other. For example: gcd and lcm (24, 54)
*find the prime factorization first and you get that
24's prime factorization is 2^3(3)
54's prime factorization is 3^3(2)
LCM = 216
GCD = 6
*In this case, 6 is a divisor of 216
2.) I think the four most important numbers in mathematics are 0, 1, 2, and 3.
0 is important because often when it is involved in some problems, the answer may be 0 or possibly undefined. i.e. whenever 0 is involved, several things cancel out because of it. 1 is also important because it is a simple number with simple rules to it..as in if it were involved in addition or subtraction, it doesn't dramatically change the solution to a problem; whereas when it's involved in multiplication or division, it doesn't change the answer at all because when multiplying or dividing a # by 1, you get that #. 2 is also important because it is the the number that can go evenly into most numbers (well I think so); especially since 2 is in the majority of categories of numbers, i.e.--2 is an integer, a whole #, natural #, even, power of 2, prime..etc. Lastly, 3 is another important number because it aquires some of the same characteristics as 2...3 is an integer, whole #, natural #, prime, odd. Also 3 is used when cubing a number or cuberooting it, as 2 is used when you want to find half of something or when you want to square a # or square root it.

Set 2:
1.) (36, 84)
*To find the gcd and lcm, you first find the prime factorization of both numbers.
36's prime fact. is 2^2(3^2)
84's prime fact. is 2^2(3)(7)
*Using the prime factorizations you find that the GCD = 12 and LCM = 252
*The product of 36 and 84 (which is also the product of the GCD & LCM) is 3024
2.) Okay for this question, I have no idea what to do because I tested it out with the gcd and lcm you gave in question 1 and it worked (because you take the product and divide it by the lcm)..but for this one I got 1/4...So I'm thinking maybe you multiply 1/4 by 1024 and get that the gcd is 256? (that's most likely wrong, but I tried..)