The title pretty much explains my question. While studying theory of numbers I came across this problem. The way I did LCM in childhood gave me a negative result.Maybe the method I used is wrong.
But according to the book, LCM(-8,20)= 40
If I use the formula LCM(a,b)= |a.b|/GCD(a,b), Then I get the right answer. But this involves finding out gcd first. Is there a direct way to solve this problem?
Thank you in advance.
An alternative to using the $\operatorname{lcm}(a,b)=\frac{|a\cdot b|}{\gcd(a,b)}$ relationship, is to break the absolute value of the numbers into their prime factors, and then multiply the highest powers of each prime (lcm by prime factorization).
For example, $|-8|=2^3$, and $|20|=2^2\cdot 5$, and so $\operatorname{lcm}(-8,20)=2^3\cdot5$.