10/10/10

Set 1, abstract:

Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?

The relationship between them is that they are both multiples or factors or divisors of each other, a and b.

Question 2.) If you were asked to state what you think to be the four most important numbers to all of mathematics. I'm not asking for your lucky 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. P.S., the answer is not 1,2,3, and 4. (Also, there are no right or wrong answers, and if you REALLY think it's 1,2,3,4, just justify your answer VERY well.)

I think the four most important numbers are 0, 1, 2, and 10. 0 because when you multiply or do anything with 0, you get zero, or nothing happens to the number you are working with. 1 because when you multiply by this you get an identity sort of answer, exactly. 2 because I seem always to be working with the number 2. You use 2 for evens and primes and stuff, and 2 is just cool lol. 10 because big numbers are "derived" from 10, like 100, 1000, 10000, etc. The power of 10 rule is also important I think, that's why I said 10 is an important number.

Set 2, concrete:

Question 1.) What is the lcm and gcd of the numbers 36 and 84? What is the product of 36 and 84?

(36, 84)

36: 2x2x3x3

2^2 x 3^2

84: 2x2x3x7

2^2 x 3 x 7

lcm: 2^2 x 3^2 x 7 = 252

gcd: 2^2 x 3 = 12

36*84 = 3024

Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?

Yaaa I honestly don't know how to do this with the information given...when this was on the test, I just left it blank lol sorry.