Out of desperation I had to create a new thread
https://math.stackexchange.com/questions/44836/rational-numbers-lcm-and-hcf
From first answer
See the writer didn't prove that the particular fraction is a LCM of the fractions so my objective in this post is to show that
lcm of (numerator of fractions) / gcd of (denom of fractions) is a common multiple and then least common multiple of two fractions.(a/b, c/d)
Lets give lcm of numerator of fraction / gcd denom of fraction a name 'k' .
Now I need to prove that this k has to be exactly divisible by both a/b , c/d Which will give me the first part of the proof.
Then I need to prove that 'k' divides any other Common multiple of (a/b, c/d)
which finally tells me that 'k' is the LCM of those two fractions.
But how to approach it.
Now from this part lcm of numerator of fraction / gcd denom of fraction
I have some information which I don't know of what help this will do in the proof.
1: I know that numerator of k is the least common multiple of a&c and it's get divided by a&c.
2: Denominator of k is the highest Common factor of (b,d) , so b & d gets divided by GCD (b,d)
Please help.
https://math.stackexchange.com/questions/44836/rational-numbers-lcm-and-hcf
From first answer
See the writer didn't prove that the particular fraction is a LCM of the fractions so my objective in this post is to show that
lcm of (numerator of fractions) / gcd of (denom of fractions) is a common multiple and then least common multiple of two fractions.(a/b, c/d)
Lets give lcm of numerator of fraction / gcd denom of fraction a name 'k' .
Now I need to prove that this k has to be exactly divisible by both a/b , c/d Which will give me the first part of the proof.
Then I need to prove that 'k' divides any other Common multiple of (a/b, c/d)
which finally tells me that 'k' is the LCM of those two fractions.
But how to approach it.
Now from this part lcm of numerator of fraction / gcd denom of fraction
I have some information which I don't know of what help this will do in the proof.
1: I know that numerator of k is the least common multiple of a&c and it's get divided by a&c.
2: Denominator of k is the highest Common factor of (b,d) , so b & d gets divided by GCD (b,d)
Please help.