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.
Sunday, October 10, 2010
10/10/10 Post (Binary FTW)
Set 1, abstract:
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
hmmm, I honestly have no clue at all
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.)
Justify briefly.
well, I'd have to say 0, 10, 100, and 1000 are probably the most important numbers in my opinion
just think about it, multiply anything times 0 and you get 0, or add anything to 0 and the sum doesn't change from the original number
as for 10, 100, and 1000, they create the easiest numbers to multiply and divide by, simple as that, as well as in addition and subtraction
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?
lcm: 252 gcd: 12 3024
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
4?
Question 1.) What is the relationship between the gcd and lcm of two positive integers, a and b?
hmmm, I honestly have no clue at all
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.)
Justify briefly.
well, I'd have to say 0, 10, 100, and 1000 are probably the most important numbers in my opinion
just think about it, multiply anything times 0 and you get 0, or add anything to 0 and the sum doesn't change from the original number
as for 10, 100, and 1000, they create the easiest numbers to multiply and divide by, simple as that, as well as in addition and subtraction
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?
lcm: 252 gcd: 12 3024
Question 2.) If the product of two numbers, a and b, is 1024 and their lcm 4096, what must their gcd be?
4?
Sunday the 10th
Well, since i read that post and i am pretty tired at the moment, I'm gonna not do this. So, I'm gonna use my homework pass.*uses homework pass*
10/10/10 omg triples
abstract:
1. I think the relationship of the GCD and LCM of a and b is that they are both multiples of a and b
2.In my opinion the 4 most important numbers in math could be 2,3,5,7 because we use prime factorization a whole lot in number theory, which applies to several types of math and these are the 4 smallest primes used for prime factorization
concrete:
1.what is the lcm and gcd of 36 and 84? what is the product?
36
2^2x3^2
84
2^2x3x7
lcm=2^2x3^2x7=252
gcd=12
36x84=3024
lcmXgcd=3024
2.(a)(b)=1024
lcm=4096
well given the information about 36 and 84 i come up with 1/4 sooooooooo... hah
1. I think the relationship of the GCD and LCM of a and b is that they are both multiples of a and b
2.In my opinion the 4 most important numbers in math could be 2,3,5,7 because we use prime factorization a whole lot in number theory, which applies to several types of math and these are the 4 smallest primes used for prime factorization
concrete:
1.what is the lcm and gcd of 36 and 84? what is the product?
36
2^2x3^2
84
2^2x3x7
lcm=2^2x3^2x7=252
gcd=12
36x84=3024
lcmXgcd=3024
2.(a)(b)=1024
lcm=4096
well given the information about 36 and 84 i come up with 1/4 sooooooooo... hah
Kaitlyn's Post 10/10/10
Set 1 abstract:
Question 1) They both find common numbers that are related to both a and b. The lcm can be divided by both a and b. The gcd can go into both a and b.
Question 2) I think the four most important numbers are 0, 1, 2, and 5. 0 because anytime you divide by 0 or multiply by 0, it will end up being no solution or 0. 1 is important because 1 can go into any number at all. When you divide a number by 1 it ends up being that number. Same when you divide by 1. 2 is important because half the numbers in the world can be divided by 2, since 2 goes into all even numbers. 5 is important because when you are dealing with prime factorization, this number shows up a lot.
Set 2 concrete:
Question 1) GCD=12 LCM= 252
The product of these two numbers is = 3024
Question 2) I think to find this you divide the product by the lcm because when i did it with question 1 it worked. So if this is how you do this, the answer would be 1/4. I dont see how thats possible but yeahhhh. But if you just divide the larger number by the smaller number, this answer would come out to be 4.
Question 1) They both find common numbers that are related to both a and b. The lcm can be divided by both a and b. The gcd can go into both a and b.
Question 2) I think the four most important numbers are 0, 1, 2, and 5. 0 because anytime you divide by 0 or multiply by 0, it will end up being no solution or 0. 1 is important because 1 can go into any number at all. When you divide a number by 1 it ends up being that number. Same when you divide by 1. 2 is important because half the numbers in the world can be divided by 2, since 2 goes into all even numbers. 5 is important because when you are dealing with prime factorization, this number shows up a lot.
Set 2 concrete:
Question 1) GCD=12 LCM= 252
The product of these two numbers is = 3024
Question 2) I think to find this you divide the product by the lcm because when i did it with question 1 it worked. So if this is how you do this, the answer would be 1/4. I dont see how thats possible but yeahhhh. But if you just divide the larger number by the smaller number, this answer would come out to be 4.
10/10/10
SET1-ABSTRACT
1) The relationship between gcd and lcm is that both a and b are either multiples or divisor of each other.
2)I think the four most important number are 2,3,5 and 7 because they are the four smallest prime numbers and they for used in prime factorization often.
SET2- CONCRETE
1)GCD(36,84)=12
LCM(36,84)=252
PRODUCT(252*12)=3024
2)I took the product and divided it by the lcm and got 1/4? so lol it might not be right
1) The relationship between gcd and lcm is that both a and b are either multiples or divisor of each other.
2)I think the four most important number are 2,3,5 and 7 because they are the four smallest prime numbers and they for used in prime factorization often.
SET2- CONCRETE
1)GCD(36,84)=12
LCM(36,84)=252
PRODUCT(252*12)=3024
2)I took the product and divided it by the lcm and got 1/4? so lol it might not be right
10/10/10
Set 1, abstract:
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.
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