alaina's blog, 10 oct. 2010

Set 1 abstract
question 1: what is the relationship between the gcd and the lcm of two positive integers, a and b?
-the gcd and lcm have common multiples and, usually, the lcm and be divided by the gcd.
for example: (40, 24)
the prime factorization of 40= 2^3(5)
the prime factorization of 24= 2^3(3)
the lcm of 40 and 24 is 120
the gcd of 40 and 24 is 8

question 2: if you were asked to state what you think to be the four most important numbers of all mathematics. i'm not asking for your luck number, or 42, or 1337, or any other quirky/"clever" response. i want to know, mathematically speaking, what you think the four most important numbers are. justify your answer.
-i really do think the four most important numbers are 1,2,3, and 4 because ,first, these are the first numbers one learns as a child. second, when added in any combination, these numbers can form all other numbers 5-10. all numbers 1-10 are the basis for all other numbers, 11-infinity.

Set 2 combination:
question 1: what is the gcd and lcm of the numbers 36 and 84? what is the product of 36 and 84?
-3squared(2squared)=36; 2squared(3)(7)=84.
the gcd of 36 and 84 is 12
the lcm of 36 and 84 is 252
the product of 36 and 84 is 3024

question 2: if the product of two numbers, a and b, is 1024 and the lcm is 4096, what must their gcd be?
their greatest common divisor is 1024.